The company had sold 54,665 units in the same month last year, it said in a statement.
In the domestic market, Hyundai sold 33,514 units last month as compared to 30,610 units in June 2013, up 9.5%.
During the month, Hyundai's exports declined by 29.3% to 17,004 units as against 24,055 units in the same period last year.
Commenting on the sales performance, HMIL Senior Vice President (Sales and Marketing) Rakesh Srivastava said the growth in the domestic sales has been due to the success of Xcent, Grand and Santa Fe.
"With the extension of excise duty benefit, we hope to maintain the growth in volume while strengthening our product portfolio and improving channel efficiencies," he added.