Southbound train No. 328 struck the pedestrian just north of the San Antonio station at about 5:25 p.m. Nobody on the train was injured.
The tracks were temporarily shut down in both directions but the northbound tracks have since reopened, Caltrain spokeswoman Christine Dunn said.
Trains are being single-tracked through the area and commuters should expect delays, she said.
"We're working as hard as we can to get the service restored because we had such a crummy morning," Dunn said.
Caltrain experienced major service disruptions earlier today when northbound train No. 101 struck an unoccupied car that had apparently been left on the tracks at Mary Avenue in Sunnyvale at about 5 a.m., Dunn said.
There were 35 passengers on that train, but no one was injured.
Both north- and southbound tracks were reopened at about 8:40 a.m.