Mukherjee said in a message: "It is with great pleasure that I convey warm greetings to you on the occasion of your birthday."
He said the multi-faceted ties between India and the UK had been expanded and strengthened in recent years.
"Our fruitful engagements and exchanges at the highest political levels have given us much to look forward to."
Born on April 21, 1926, Elizabeth II, the world's oldest living and Britain's longest-lived monarch, was coronated on June 2, 1953.
According to the British royal family's website, Queen Elizabeth II celebrates two birthdays: her actual birthday on April 21 and her official birthday on (usually) the second Saturday in June.