Former champions Lleyton Hewitt, Venus Williams and Serena Williams are also in action, while Belgian fourth seed Kim Clijsters, the favourite for the women's title, meets Ai Sugiyama of Japan for a place in the last 32.
World number one and defending champion Federer, who is bidding to win his sixth grand slam title, meets the wily Fabrice Santoro.
Federer has won six of their eight previous meetings and dropped just four games in beating the Frenchman in the first round at the Australian Open in January.
Australian Hewitt, the 2001 champion, meets Jose Acasuso of Argentina, while sixth seed Nikolay Davydenko of Russia and David Nalbandian, the 11th seed from Argentina, are also in action.
Russian Sharapova, who has never been past the third round in New York, meets Julia Schruff of Germany, and Serena Williams, the Australian Open champion and eighth seed, takes on Italian Francesca Schiavone, the 25th seed.
Wimbledon champion Venus Williams kicks off the night session when she faces Slovakian Daniela Hantuchova, the 20th seed, having won all seven of their previous meetings.
