"Following a clash this morning in training Morata suffered serious cranial trauma," Milan said in a statement.
"He was rushed to hospital where an MRI scan was negative. Alavaro is feeling better and will stay in hospital under observation."
Italian media report that Morata, who scored in Milan's stunning 3-1 Champions League win at Real Madrid on Tuesday, was hurt during a battle for the ball with defender Strahinja Pavlovic.
Morata has scored three times for Milan since returning to Serie A this summer after winning Euro 2024 with Spain.
Milan are seventh in Italy's top flight and eight points behind league leaders Napoli ahead of Saturday's match at Cagliari, albeit with a game in hand.
