Police want to question the men over the 1989 killings in the Central American country during its civil war.
The murder was among the most notorious incidents of the violence. Military authorities apparently saw the priests as leftist sympathisers.
El Salvador's national police force said that the four were arrested at the behest of Interpol.
They are named as Colonel Guillermo Alfredo Benavides Moreno and soldiers Antonio Ramiro Avalos Vargas, Angel Perez Vasquez and Tomas Zarpate Castillo.
It is up to El Salvador's Supreme Court to rule on the extraditions to Spain.
On Friday, a US judge cleared the way for another former Salvadoran colonel to be extradited to face charges in Spain in the case.