Step 1: Foot drop means failure to lift the forefoot, which is an anterior-compartment dorsiflexor problem.
Step 2: Those dorsiflexors get their motor supply from the deep branch of the common peroneal (common fibular) nerve. Knock out that nerve and dorsiflexion fails.
Step 3: The nerve is most vulnerable as it crosses the lateral neck of the fibula, where pressure, fractures, or surgery readily damage it, making it the classic site of foot drop.
Step 4: Among the options, the tibial nerve handles plantarflexion, the femoral nerve handles knee extension, and the sciatic injury is proximal and broad; the precise culprit for an isolated foot drop is the common peroneal nerve.
\[\boxed{\text{Common peroneal nerve}}\]