"The striker sat out this morning's session at Tottenham Hotspur's training ground as a precaution due to a minor knee injury," the FA said.
"Rooney has been allowed to return to his club for further assessment."
England's interim manager Gareth Southgate had earlier said that Rooney would be rested from the starting line-up in any case, with Liverpool's Jordan Henderson filling in as captain.
Rooney returned to England's starting XI for Friday's 3-0 win over Scotland in World Cup qualifying, having started the previous game -- a 0-0 draw away to Slovenia -- on the bench.
Left-back Ryan Bertrand, who also missed training on Monday, remains in contention to feature in the game at Wembley.
Harry Kane had already been ruled out of Tuesday's match, the Tottenham striker having returned to his club as he continues his recovery from an ankle ligament problem.
The game against Spain is the fourth and final match of Southgate's tenure as interim manager, but he is expected to be offered the role full-time.