Yes. This happened to multiple ethnic groups across several years, though the amount of replacement by ethnic Russians varied.

The first major deportation came in 1937, when the ethnic Korean population of Russia (about 172,000 people) were removed from the Soviet Far East (near the modern Russia-North Korean and Chinese borders) into Central Asia, mainly what is modern Kazakhstan and Uzbekistan. This was ostensibly done for security concerns: mainland Korea was part of the Japanese Empire at the time, and the USSR and Japan were both gearing up for war, which finally broke out between them in 1939 (though they ended up with a ceasefire that lasted until 1945).

The next major wave of deportations would come in September 1941, with the Volga Germans being moved to Central Asia (Kazakhstan and Kyrgyzstan, for the most part). This constituted about 340,000 people, and was the first deportation linked to the Nazi German invasion of the Soviet Union (which started in June 1941): the Soviet leadership (read: Stalin) felt that the ethnic Germans would collaborate with the invaders (never mind that the Volga Germans had been living in Russia for nearly two centuries by that point).

In 1943 and 1944 further deportations were orchestrated: the Germans briefly occupied parts of the North Caucasus (directly south of Stalingrad), and there were, and are, many ethnic groups living in that region, many of whom did not like the Russians. Assumed of being collaborators under the German occupiers (though in some cases the Germans never even reached their territory), groups of peoples were forced out:

In a series of bold moves the Karachays (November 1943; 70,000 people), Kalymyks (December 1943; 93,000), Balkhirs (March 1944; 37,000), Meskhetian Turks (November 1944; 90,000) were all sent to Central Asia. Once Crimea was reoccupied in 1944, the Crimean Tatars were also sent away: 190,000 people were moved to Uzbekistan, and the region was repopulated with ethnic Russians: the 1939 census had the population at 19% Crimean Tatar and 50% Russian; the 1959 census had it at 0% and 71%, respectively (the 2001 Ukrainian census, the only one taken with Crimea, had it at 68% and 13%).

However what is probably the most famous event of the Soviet deportations came on February 23, 1944. Codenamed Operation Lentil (Чечевица, Chechevitsa, in Russian), at least 495,000 Chechen and Ingush (closely related to the Chechens) people were forced out of their home, and within about 3 days were gone. This was by far the largest deportation in terms of number, and arguably had the most long-ranging consequences (the Chechen wars of the 1990s and 2000s can arguably be partially traced back to this event).

In the North Caucasus the territory was filled with ethnic Russians, though with the death of Stalin in 1953 and the rise to power of Nikita Khrushchev in 1956 this policy was slowly relaxed. Some peoples, like the Chechens were allowed back to their homeland in 1957, while others like the Crimean Tatars, were forced to wait for the USSR to collapse before they could move back.

There are several worthwhile books on the subject:

• Stalin's Genocides by Norman M. Naimark (2011). Naimark is one of the leading scholars on European genocide and ethnic cleansing, and this short book (about 200 pages) is probably a good introduction to the topic.

• Against Their Will: The History and Geography of Forced Migrations in the USSR by Pavel Polian (2004). A more comprehensive look at not just the deportations, but all population transfers in the USSR (including the kulaks and occupied territories). I haven't read through it all, but it's worth taking a look at.

• Let Our Fame Be Great: Journeys Among the Defiant People of the Caucasus by Oliver Bullough (2010). A journalist, not a scholar, Bullough worked in Russia for some time, and spoke to several survivors of the North Caucasian deportations from a variety of ethnic groups in this book. It is a really difficult read because of the subject matter, but very powerful and very worthwhile.

• Ethnic Cleansing in the USSR, 1937-1949 by Otto J. Pohl (1999). Pohl is another scholar who works on the deportations and ethnic cleansing in the Soviet Union. This is a very serious academic book, full of statistics and data like that. However he's also written several journal articles on the topic, particularly about the Volga Germans, so is worth looking into.

• Burnt by the Sun: The Koreans of the Russian Far East by Jon K. Chang (2016). As the title suggests, Chang looks at the Korean population living in Russia, and includes quite a bit on their deportation. I have not read the book though, so cannot confirm the details first-hand (although I understand it's received favourable reviews).

• The Punished Peoples: The Deportation and Fate of Soviet Minorities at the End of the Second World War by Aleksandr Nekrich (1978). Probably one of the first books on the subject, by a Russian-American historian. It will be quite dated now, so I would not recommend reading this before more recent work, but it is still valuable.

And a couple journal articles:

• "An Early Soviet Ethnic Deportation: The Far-Eastern Koreans" by Michael Gleb, in The Russian Review Vol. 54, No. 3 (July, 1995), pp. 389-412. This predates Chang's book by some time, and was one of the first real looks in English at the topic.

• "Deportation of the Kalmyks (1943–1956): Stigmatized Ethnicity" by Elza-Bair Guchinova, in Empire, Islam, and Politics in Central Eurasia edited by Uyama Tomohiko (2007). Guchinova looks at the Kalmyks and how they tried to re-integrate back into their homeland after the deportation.

• "The Origins of Soviet Ethnic Cleansing" by Terry Martin, in The Journal of Modern History, Vol. 70, No. 4 (December, 1998), pp. 813-861. I would be amiss to not cite Martin in one of my posts, so here he is. This large article (50 pdf pages) looks at the background of the whole subject, and is important to understanding the whole thing.