The 23-year-old has ruptured a pectoral muscle, which will take up to 16 weeks to heal following surgery.
"It is hugely disappointing for Rhodri, who was working extremely hard out in Switzerland. We wish him all the best with his recovery from the injury," Wales head coach Warren Gatland said in a statement.
"It is a great opportunity for Scott to come into the squad and show us what he is capable of. In terms of the tighthead position, Samson [Lee] has continued to make excellent progress and we have been very impressed with both Aaron Jarvis and Tomas Francis during the first batch of training."
Andrews, who has previously represented Wales on 11 occasions, will link up with the squad for their trip to Qatar this weekend.