Defender D'Ambrosio was introduced as an 81st-minute substitute against Samp and was on the end of a strong challenge from Mehdi Leris deep into stoppage time.
The 32-year-old's leg appeared to buckle under the tackle and he was left in clear pain, although medical staff were able to help the player to his feet to walk off the pitch in the final moments of the 2-1 defeat – Inter's first in nine matches.
A statement on Thursday detailed the nature of the injury after medical tests.
"His condition will be reassessed next week," the Nerazzurri said.
Wednesday's match was D'Ambrosio's 11th appearance of the season, of which only four have been starts. He has scored three goals from defence but contributed to just a single clean sheet.