The Chelsea striker has started the campaign in superb form, scoring nine goals in seven Premier League appearances following his switch from Atletico Madrid.
Costa, though, has been consistently troubled with a hamstring problem, with club boss Jose Mourinho suggesting his training has been limited and he should not play three games in quick succession.
The Portuguese made it known that he wanted Costa to skip the international break in order to have a prolonged rest, but Spain coach Vicente del Bosque opted to name him in his 23-man squad.
Having failed to score in five appearances since switching his allegiance to Spain from the country of his birth Brazil, Costa - who turned 26 on Tuesday - will be desperate to hit the target in Zilina.
However, Costa is not guaranteed to start after Valencia's Paco Alcacer scored on his first Spain start in their opening pool match with Macedonia last month, which finished 5-1 in Spain's favour.
Alcacer's club-mate Rodrigo is another forward option after he earned his first senior call-up, while Bayern Munich's versatile left-sided player Juan Bernat could also make his international bow.
Bernat is desperate to impress and insists he is will play anywhere for the team.
"Right now I’m playing more as a full-back, but I’ve spent my whole life playing on the wing; I will play wherever I’m needed," he said.
One man who will not feature for the reigning European champions is Real Madrid defender Sergio Ramos - who withdrew with a calf injury on Monday - with Barcelona's Marc Bartra taking his place in the squad.
The inclusion of Bartra's club-mate Gerard Pique has caused some controversy, as questions were raised over his commitment to Spain after he backed calls for Catalonia to hold a vote on independence.
However, Barca forward Pedro insists Pique is fully behind Spain's cause, saying: "Pique is eager to help the team. With the national team he always plays at a high level."
In Slovakia, Spain face a side positioned 32 places below them in the FIFA world rankings.
But since Jan Kozak was appointed head coach in July 2013, Slovakia have lost just three times in 11 matches - winning five of their past six outings.
They started their qualifying campaign with a fine 1-0 success in Ukraine and Robert Mak, who scored the winner in that game, insists Slovakia do not fear Spain.
"We aren't going to stand there and stare at the Spanish players," he said.
"We want to compete with them and try to make things difficult for them."
