Real Madrid defender Ramos was named in Vicente del Bosque's 23-man party for Spain's Group C matches at Slovakia and Luxembourg this week.
However, he will leave Spain's training camp after tests on the injury revealed he would not be fit enough to play.
Barcelona's Bartra has subsequently been drafted in to deputise.
"Sergio Ramos is ruled out for the matches against Slovakia and Luxembourg," read a statement on the Spain national team's official website.
"Centre-back Ramos will leave the training camp due to a calf injury in his right leg.
"The player has undergone medical tests in the Sanitas La Clinica Moral. Marc Bartra will join up the squad today."
Spain opened their European Championship qualifying campaign with a 5-1 demolition of Macedonia last month.
Arsenal prepared to replace star forward, in shock move following Saudi offer: report
'Too little, too late - Bruno Fernandes didn’t sho leadership so it’d be interesting to hear what Erik ten Hag has to say about his apology': Everything Roy Keane said about the Manchester United captain after Chelsea draw
