The Juventus midfielder started as Les Bleus came back from 2-0 down to beat Belgium 3-2 in the semi-finals, coming off for Monaco's Aurelien Tchouameni with the scores level in the 75th minute.
Yannick Carrasco and Romelu Lukaku struck in the first half but Karim Benzema and Kylian Mbappe hauled France level before Theo Hernandez hit a dramatic winner in the 90th minute.
However, Rabiot will not be able to participate in Monday's (AEDT) showdown in Milan and is now in isolation away from the rest of the squad.
The news of the midfielder's unavailability will come as a blow to France boss Didier Deschamps, who has already lost left-back Lucas Digne to a hamstring injury and was unable to call up N'Golo Kante for the tournament, with the Chelsea star having also contracted COVID-19.
France is unable to name replacements for the pair and will be forced to face Spain at San Siro with a 21-man squad.