Yes. Slaves from East Africa and Madagascar were imported to India, both by European powers like Portugal and Netherlands, but also by Gujarati merchants, Omani, and Swahili traders.

For literature about the topic I'd recommend the following works-

"A Forgotten Corner of the Indian Ocean: Gujarati Merchants, Portuguese India and the Mozambique Slave Trade, c.1730–1830" by Pedro Machado, in Slavery and Abolition; a journal of slave and post-slave societies vol 24:2 pp 17-32.

Also, Jonathan Walz and Stephen Brand's chapter "Archaeology of the Other Diaspora; the slave trade and dispersed Africans in the Western Indian Ocean " in African Re-Genesis edited by Haviser and MacDonald. pp 246-268.

Slaves, Spices and Ivory by Abdul Sheriff touches on the role of Indian merchants in the economy of Zanzibar, particularly with respect to the East African slave trade and ivory trade.

Sailors, Slaves and Immigrants; bondage in the Indian Ocean World 1750-1914 by Allesandro Stanziani touches on enslaved Africans who were liberated by Anti-Slave patrols in the Indian ocean and brought to Bombay as personal servants.

For a slightly different perspective, you could take a look at:

"The Mascarene Slave-Trade and Labour Migration in the Indian Ocean during the Eighteenth and Nineteenth Centuries" by Richard B Allen in Slavery and Abolition vol 24:2 pp 33-50

Which covers French sugar plantations in Seychelles and Mauritius islands which used slaves from East Africa, Madagascar and from India.

Since u/Commustar has provided 18th-19th century sources, I'd like to talk a bit about earlier times.

There was a major trade in Habshi (meaning Abyssinian) slaves from the Horn of Africa to the Islamic polities of India in the Late Medieval and Early Modern periods. Unlike in the Atlantic slave trade, however, these slaves were generally not bound for agricultural work but for domestic and military service, similar to mamlukes and janissaries elsewhere in the Islamic world. And just like those groups, these African slave-soldiers often ended up in positions of power, even coming to rule at times in places like Bengal and the Deccan. To give a sense of scale, there were reportedly some 40,000 African soldiers in Delhi already during the 14th century.

The Portuguese Tome Pires, for instance, wrote of 'Abyssinians' ruling Bengal around 1515 AD;

They are considered in these parts to be loyal, true and faithful knights, and often from being slaves they rise to be kings, chiefly in Bengal.

The king [of Bengal] is a Moor [meaning Muslim], a warrior. He has great renown among the Moors. The people who govern the kingdom are Abyssinians. These are looked upon as knights; they are greatly esteemed; they wait on the kings in their apartments. The chief among them are eunuchs and these come to be kings and great lords in the kingdom. Those who are not eunuchs are fighting men. After the king it is to this people that the kingdom is obedient from fear.

They have now been following the Pase practice in Bengal for seventy-four years, that whoever kills the king become king. They hold and believe that no one can kill the king without the consent of God, and he therefore becomes king; and in this way the kings last a very short time. From that time up to now it has always been Abyssinians—those who are very near to the king—who have reigned.

In the Deccan Sultanates Habshi, also known as Siddi (apparently an honorific term), came to a similar degree of prominance, most notably with the rise of Malik Ambar, de-facto ruler of the Ahmednagar Sultanate in the early 1600s, who founded the modern city of Aurangabad and succesfully resisted Mughal conquest, apparently pissing of Jahangir enough that he commisioned a painting of Ambar's head on a pike. He also granted the island fortress of Janjira to some of his Siddi followers, who would come to rule the Sultanate of Janjira from 1621 until 1948. After the fall of Ahmednagar, Janjira would hold out against the rising power of the Marathas and, as Mughal allies, defeat the English in Child's War of 1689.

So, to say the least, African slaves and their descendants have played a major role in Indian history. There remains today a large Siddi/Habshi diaspora some quarter of a million strong, mostly scattered in ethnic enclaves in Gujarat, Karnataka, Hyderabad and along the western coast around Mumbai and Goa.

Yimene, Ababu (2007) 'Dynamics of Ethnic Identity Among the Siddis of Hyderabad', African and Asian Studies Vol. 6, pp. 321-345.

Jasdanwalla, Faaeza (2011), 'African Settlers on the West Coast of India: The Sidi Elite of Janjira', African and Asian Studies Vol. 10, pp. 41-58.

Tomé Pires (1515), Summa Oriental

A great lecture by Kenneth X. Roberts on 'African Elites in India'