Dr Woods of Pembroke College was being treated by the medical crew but was said to be conscious and sitting up.
One of the Oxford rowers was carried out of the boat after he collapsed at the end of the race.
Medic Alexander Woods, 27, was lifted from the bow.
Because of this, there was no presentation to the winning team.
The University Boat race restarted but Oxford broke an oar a few seconds later following a collision between the boats. Cambridge raced away to win comfortably.
The 158th Boat Race between Oxford and Cambridge was brought to a halt today by a man swimming across the Thames.