Martin is set to undergo surgery on his left hand on Tuesday to stabilise the fractures and recovery time will be assessed post-surgery.
"Jorge Martin suffered a complex fracture of the radius, some carpal bones on the left side and an ipsilateral calcaneal fracture during a training session," Aprilia said in a statement.
"After a surgical consultation, it was decided to proceed with surgery, which will take place tomorrow at the Dexeus Clinic in Barcelona."
Martin had undergone surgery earlier this month after breaking his right hand and foot in a nasty crash in Sepang, Malaysia.
According to Spanish media reports, Martin was due to receive medical clearance to compete at Thailand's Chang International Circuit on Friday before suffering the accident while training at the Menargues karting circuit in Spain.
Aprilia said test rider Lorenzo Savadori will replace Martin in Thailand.