The Chelsea striker was forced out of the session with a foot and ankle injury and subsequently underwent X-rays at the Sanitas Clinic in La Moraleja.
Costa was passed fit by doctors from the Spanish Football Federation, who informed Chelsea of Costa's condition, and he will remain with the national team for Tuesday's international friendly against France in Paris.
Spain's medical staff will continue to monitor the 28-year-old's condition. Costa played and scored in his country's 4-1 World Cup qualifying win over Israel last Friday, playing the full 90 minutes.
The former Atletico Madrid striker has consistently been in the goals this season, scoring 22 in 35 appearances for club and country.
Costa's goals have helped Chelsea establish a healthy lead at the top of the Premier League table, with Antonio Conte's side currently boasting a 10-point advantage over closest challengers Tottenham Hotspur.
Chelsea will resume their march towards the title with a visit from Crystal Palace on 1 April, before entertaining 3rd-placed Manchester City the following Wednesday.
Additional reporting by PA