Morata picked up the problem during the Blues' defeat against Manchester City on 30 September and has withdrawn from the Spain squad for the World Cup qualifiers against Albania and Israel.
Batshuayi, who has only made one start in the league for Chelsea this season and is yet to find the back of the net, said he was focused on making the most of his opportunity to play in the first team.
"It sounds strange to say, but someone's bad luck is sometimes the happiness of the other," the Belgium striker told Sky Sports.
"I know that I will have more playing opportunities in the coming weeks. It's up to me to show that I'm capable. I know [Chelsea manager Antonio] Conte has confidence in me. Otherwise, he would have let me leave during the summer.
"It's a chance for me. If I'm called on, I want to be ready and efficient. I have to stay really focused.
"I've already started games at Chelsea and played well. I'm an efficient striker, but I'm not a joker."
Batshuayi joined Chelsea from Marseille on a five-year deal last summer in a transfer that was worth £33m ($44m).
He played second fiddle to Diego Costa at Stamford Bridge last season, scoring five times in 20 Premier League appearances.
The 24-year-old has been called up to the Belgium squad by Roberto Martinez for the World Cup qualifiers against Bosnia and Herzegovina and Cyprus.
Morata, a £60m summer signing from Real Madrid, is Chelsea's leading scorer this season with seven goals.
The Spain striker was replaced by Willian after he was forced off during the first half of Chelsea's Premier League clash against City, with Eden Hazard taking up a more central role.