It seems that would have been a fairly easy way to assist their German allies. The Soviet Navy was not a terribly strong one, whereas the Imperial Japanese could have had the strongest navy in the world in 1941. It wouldn't have taken much of the IJN to seal off that port, and I don't think the Soviet navy had anywhere near the strength to break the blockade.
With Vladivostok blockaded, the USSR would be cut off from a major landing point for lend-lease supplies, which I imagine would have hurt them significantly.
So why not? Was the IJN just too thinly spread to try, or did they simply have no interest at all in helping the Germans?
Japan was not at war with the USSR until the Soviets invaded Manchukuo on August 9th 1945.
In 1939, Japanese and Soviet land forces engaged each other in a series of battles known collectively as the Battles of Khalkhin Gol. This was not the first skirmish to take place along the borders between Manchukuo (the Japanese puppet state in Manchuria), the USSR, and communist Mongolia, however, Khalkhin Gol ended in a Soviet/Mongolian victory that was significant enough to dissuade the Japanese Army from further antagonizing the USSR.
In April 1941, the Empire of Japan and the USSR signed the Soviet–Japanese Neutrality Pact in which they agreed to avoid further border conflicts. The Soviets promised to respect the territorial integrity of Manchukuo, whilst Japan promised to respect the territorial integrity of the Russian Far East and the Mongolian People's Republic.
Japan was already bogged down in a war in China at that point, and Japanese leaders were preparing for a potential war against the United States, United Kingdom, and the Netherlands. Peace with the Soviets was therefore desirous, as it would free up military resources to be used elsewhere. War with the USSR would directly threaten Manchukuo (which was rather important for Japan's economy) and Japanese conquests in China. Following the German invasion of the USSR in June 1941, the Neutrality Pact turned out to be pretty beneficial for the Soviets as well, as it allowed them to transfer experienced troops from the Far East to the west in order to fight the Germans.
However, at the Yalta Conference Stalin had promised the Western Allies that the USSR would enter the war against Japan three months after the end of fighting in Europe. In April 1945 the Soviet Union denounced the Neutrality pact, and on August 9th they invaded Manchukuo. The declaration of war was handed to the Japanese ambassador at Moscow after the invasion began, but due to time zones, it was technically delivered on August 8th, precisely three months after Germany's surrender.
Soviet forces quickly overwhelmed the Kwantung and Manchukuo Armies, and the Japanese navy by this point had been almost completely destroyed in the fighting in the Pacific. A blockade of Vladivostok would not have been anywhere near possible.