As an employer, you can extend a probationary period for many reasons, and an injury would be one of them. Of course, we are assuming that the injury was on the job. As an employer, you can also terminate for any reason during the probation period. However, if this injury was on the job and the injury is causing performance issues, you may be at risk for a wrongful dismissal.
Just because an employee is on probation does not mean they shouldn’t be given progressive discipline, maybe this is an opportunity to start there.
However, maybe the injury was relatively minor, and you only needed to accommodate for a short period of time, in which case there is absolutely no causal link between performance and the injury, and termination would be entirely appropriate.