The Brazil forward was replaced by compatriot Kaka at half-time during Saturday's 3-1 defeat at Napoli in Serie A.
And the 30-year-old former Real Madrid man looks unlikely to feature against Diego Simeone's men for the first leg at San Siro next Wednesday.
"Robinho has sustained a muscular injury in his left thigh," a Milan statement read.
"The Brazilian striker will undergo further tests next week."
Robinho's injury is a blow for Milan coach Clarence Seedorf, whose side will be underdogs for the clash with the La Liga title contenders.
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