The club denied reports that the famously temperamental 29-year-old player, who was taken ill on the flight back from the 3-2 win at AS Roma on Saturday, had suffered a stroke.
"AC Milan inform that the news in circulation containing a hypothetical diagnosis on Antonio Cassano's state of health cannot be considered true as it does not come from an accredited medical source," Milan said in a statement.
"AC Milan underline that Antonio Cassano is in a phase of marked improvement and in the next few days will undergo further medical examinations."
While Cassano, who appears to have matured and settled down well since joining Milan at the start of the year, was confined to a clinic, Milan left for Belarus where they play BATE Borisov in a Champions League match on Tuesday.
A win could guarantee Milan a place in the last 16 with two games to spare depending on the result of the Viktoria Plzen-Barcelona game.
"I know that he feels better and I hope to have him back with us soon. He is resting and I have felt that he is calm," coach Massimiliano Allegri told reporters before the team left Italy.
"The team is calm but disappointed at what his happened. From the human point of view, it's always disappointing especially when it happens to a lad of 29.
"Antonio has been playing really well but the important thing now is to rule out that it's anything dangerous."
Bari-born Cassano has previously played for AS Roma and Real Madrid in a career marked by tantrums and personality clashes.
Later, in Belarus, Allegri told the pre-match media conference: "We will play for Antonio. There are so many other aspects apart from the sporting ones and we're all saddened."
