Cruyff was diagnosed with lung cancer in October, but recently stated that he felt "2-0 up" in his battle against the illness.
However, he passed away in Barcelona on Thursday, surrounded by his family.
Infantino has now joined the outpouring of tributes to Ajax and Barcelona great Cruyff, describing him as a "symbol of elegant play".
"Johan Cruyff was a magnificent player, one of the greatest players the world has ever known," Infantino said via a statement on FIFA's website.
"Cruyff was a symbol of elegant play. An inspiration. A source of admiration for fans. He has marked football history forever.
"I'm very saddened by his death. He will be terribly missed.
"Both personally and on behalf of FIFA and the world football community, I would like to extend my sincerest condolences to his family and friends."
Cruyff won eight Eredivisie titles during his first spell as a player at Ajax, as well as three consecutive European Cups in the 1970s.
He went on to enjoy further success at Barcelona, winning La Liga and the Copa del Rey as a player before leading the Camp Nou side to four straight league titles in the 1990s.