De Bruyne appeared to pull a muscle as he converted a first-half penalty, immediately clutching the back of his right thigh. The former Manchester City player looked distraught and had to be helped off the field by two medical staff.
Scott McTominay and Frank Anguissa also scored for Napoli after the break, either side of an Inter penalty converted by Hakan Çalhanoğlu.
Saturday's win lifted Napoli a point above second-placed AC Milan, who drew against Pisa on Friday.
Inter, who had been on a seven-match winning run, are fourth.
Napoli were already struggling with injuries and their problems got worse when De Bruyne was forced off.
The penalty had been awarded after Inter midfielder Henrikh Mkhitaryan was adjudged to have fouled Giovanni Di Lorenzo. Mkhitaryan also went off injured.
Inter came close to levelling the match in the dying seconds of the first half as Alessandro Bastoni hit the crossbar and Denzel Dumfries clipped the post.
McTominay doubled Napoli's lead in the 54th minute following a rapid counterattack.
Çalhanoğlu reduced the deficit five minutes later with a penalty but Anguissa restored Napoli's two-goal advantage when he finished off another clinical counterattack.
Udinese beat Lecce 3-2 for their first home win since March 1.
Jesper Karlström, Keinan Davis and Adam Buksa scored for Udinese, who had picked up just two points in their previous four matches.
Como were held to a 0-0 draw at Parma.
14°C