Medics were called to the intersection of 5th Ave. N. and Harrison Street just after 2 p.m., fire officials said.
A witness told KOMO News the van was turning off 5th to go east on Harrison when it struck the bicyclist. The bicyclist then had a seizure in the crosswalk.
Medics arrived and found the woman conscious but disoriented. They took the woman to Harborview Medical Center with serious but non-life-threatening injuries. Officials said the bicyclist was wearing a helmet.
The driver of the van was pregnant and she too was being taken to a local hospital to be checked out.
Seattle police are investigating the crash.