"The national team centre back Sergio Ramos will leave the training camp after tests revealed an injury in the calf muscle in his right leg," Spain said on their official website (www.sefutbol.com).
Barcelona defender Bartra will join up with the rest of the squad later on Monday, they added.
Ramos, who has made 121 appearances for La Roja, had to be replaced at halftime during Real Madrid's 5-0 win at home to Athletic Bilbao on Sunday (local time).
He said earlier on Monday he was optimistic he could feature in the two qualifiers but his withdrawal means Raul Albiol is likely to partner Gerard Pique in central defence instead.
Spain are looking to follow up their 5-1 success at home to Macedonia in their opening Group C match.
If they qualify as expected from a pool that also includes Ukraine and Belarus, the 2010 world champions will be chasing a third consecutive continental title in France in two years' time.
They play Slovakia in Zilina on Thursday and take on Luxembourg in Luxembourg City on Sunday.
There are two new faces in coach Vicente del Bosque's squad: forward Rodrigo, who is on loan at Valencia from Benfica, and Bayern Munich left back Juan Bernat.
Brazil-born Rodrigo, who played for Real Madrid and Spain at youth level and is a cousin of Bayern's Spain midfielder Thiago Alcantara, said he was determined to make the most of the experience.
"We all know how difficult it is to get here," the 23-year-old told reporters.
"Spain is one of the best teams in the world, if not the best, and it takes a lot to make it into the squad.
"I am here to enjoy the football and the experience and give the best of myself."
Rodrigo is behind Chelsea striker Diego Costa and Valencia team mate Paco Alcacer in the pecking order up front and is unlikely to start either of this week's matches.
