The bomb detonated in a car park at the University of Navarra, breaking windows and setting other vehicles on fire, said Amaya Zaratiegui, a spokeswoman for the university's clinic.
Navarra is a northern region of Spain of which Pamplona is the capital.
Aparicio Caicedo, a 29-year-old Ecuadoran who is doing doctoral work at the university, said he was studying in the library, near the car park when the bomb went off.
"Suddenly the whole building shook and there was a huge column of smoke. It was tremendous, a huge explosion,'' Caicedo said.
He said the bomb went off at a time when many students and other people were walking by the area ofthe explosion.
Television footage showed a university building on fire at the ground floor level and spewing thick black smoke.
The Spanish interior ministry office in Pamplona said the wounded were apparently cut by flying glass.
Yolanda Barcina, Pamplona's mayor, told Spanish radio she was surprised the casualty toll from the blast was not higher.
"We got lucky with the weather. It is raining, and there were fewer people than usual outside,'' she said.
Eta has killed more than 800 people since the late 1960s in its campaign to create an independent Basque homeland in northern Spain and southwest France.
Navarra borders on the Basque region and is home to many Basque speakers.