"The first team player Thomas Vermaelen felt a problem in Sunday's game away at Levante. Tests carried out on the defender show that he has a torn muscle in his right calf and will be out for around 4 weeks," the club said in a statement on their official website.
The Belgium international started Sunday's 5-0 La Liga win over Levante. However, he was replaced by Arthur on 52 minutes at the Estadio Ciudad de Valencia.
Vermaelen's injury leaves Barcelona short of options at centre-back. Samuel Umtiti is currently sidelined and undergoing treatment in Qatar for a knee problem, per Sport.
The injuries mean manager Ernesto Valverde has only two fit senior centre-backs to choose from at present in Gerard Pique and Clement Lenglet.
Samuel Marsden at ESPN FC said Barcelona could look to sign a defender in January:
Vermaelen is very much a back-up option at Barcelona. He's managed just three La Liga starts this season and is behind Pique, Umtiti and Lenglet in the pecking order.
The 33-year-old's time at Barcelona looks to be coming to an end. His contract expires in the summer, and he's said he is open to a return to the Premier League.
"It is not impossible," he told the AFP (h/t Marca). "I have warm memories of my time in England and I was very happy there."
Vermaelen has been plagued by injuries since joining Barcelona from Arsenal in 2014, and it seems unlikely the club will offer him a contract extension.
The Spanish champions are also being heavily linked with a move for Ajax captain Matthijs de Ligt. Barcelona have made signing the centre-back their top priority next summer, according to Sergi Capdevila at Sport.