Northbound train No. 305, which departed from San Jose, struck the person about 30 feet north of the Oak Grove Avenue pedestrian crossing at approximately 6:23 a.m.
The pedestrian was pronounced dead at the scene, she said.
Trains were initially stopped in both directions, then allowed to single-track through the area. At about 8:25 a.m., the tracks reopened in both directions and trains returned to normal speed.
Riders should expect 30- to 90-minute delays, Caltrain spokeswoman Tasha Bartholomew said.
A SamTrans bus bridge has been set up between Caltrain's Millbrae and San Mateo stations, and both SamTrans and BART are honoring Caltrain tickets.
The Martin Luther King Jr. Freedom Train is expected to leave San Jose's Diridon station at 9:30 a.m. as scheduled.
The death marks the second fatality on Caltrain tracks since the beginning of the year, Bartholomew said. Eleven people died on Caltrain tracks in 2010, down from 19 in 2009.