The pair were both substituted during the clash at San Siro on Sunday and the double injury blow leaves Roberto Mancini with a selection headache.
Andreolli was first to depart just before half-time as he pulled up inside the penalty area and D'Ambrosio followed him back to the changing room 10 minutes after the break
Inter confirmed the extent of their injuries via their official Twitter account on Monday, but offered no timescale for their recoveries.
With Juan Jesus, Yuto Nagatomo and Jonathan already sidelined, Inter coach Mancini is running out of defensive options, although Andrea Ranocchia was able to return against Torino.
There were fears that the 26-year-old could have damaged knee ligaments against Empoli earlier this month, but scans were clear and he was able to play the entire second half.
