The former Arsenal striker began the tests at Barcelona Hospital at 10 a.m. (0800 GMT) and later continued them at the Camp Nou stadium with no signs of problems, the club said.
Henry, 29, arrived at FC Barcelona on Sunday after the Catalan club agreed to pay Arsenal EUR24 million (16 million pounds; US$32 million) for the France striker in a four-year deal.
Henry leaves Arsenal as the club's top scorer, with 226 goals in 364 appearances. He helped the London team to two Premier League titles, three FA Cups and the 2006 Champions League final, which it lost to Barcelona.
He missed much of last season because of stomach and groin injuries.
At Barcelona, he joins two-time FIFA player of the year Ronaldinho, Cameroon striker Samuel Eto'o and Argentina winger Lionel Messi.
Barcelona, coached by Dutchman Frank Rijkaard, was runner-up to champions Real Madrid in the Spanish first division this season.