Medical discharge in the Roman army was called missio causaria, which can be reliably documented in the 3rd century AD and was probably introduced during the Principate. Aemilius Macer, a jurist in the 3rd century states that early discharge from the army was granted to a soldier who was 'no longer fit to serve due to some defect of mind or body.'
There are several hypotheses on what exactly the missio causaria entailed, and how it differed from missio honesta, the honorable discharge of veterans. Davies, Campbell and Grassl postulate that the privileges of the invalided discharge and full-term discharge was identical at first, comprising of the right to marry, citizenship, some land or money, exemption of taxes and so on. Diplomas dated to the 1st century AD were found in which several veterans were classified as causarii, and also granted an honesta missio simultaneously. In another example, Pompey founded the city of Nicopolis after the Mithridatic Wars and populated it with his veterans together with 'the soldiers who had become unfit for service.'
The ad-hoc veterans' grants of the late Republican period was probably first given a set of rules under Augustus, and the medical discharge was first codified as a reason for dismissal. It seems that prior to 213 AD, the causarii were treated as a part of the broad veteran community and considered to be honorable discharges with same status and privileges.
However, in 213 AD, Caracalla decided that only causarii who had served at least 20 years were entitled to the same privileges of the honorable discharge, which also indicates that from then on, medical discharge was not simply seen as a cause for honorable discharge, but a whole different category from the full-term discharge (emeriti). Later on, Constantine would issue even stricter regulations concerning grants for medical discharges, stating in 325 AD that only ripenses (frontier garrison soldiers) who had been wounded in battle will be rewarded.
So, if you are a invalided soldier in the early Empire era, chances are that you'll be given a honorable discharge similar to the full-term discharge, and granted lands like many of Augustus' veterans. If somewhat earlier, during the late Republic era, the specifics will more depend on who your commander is (because of the nature of privatised armies) but you'll likely get a similar deal of land grants and veteran settlements.
Some sources are :
JB Campbell, The Emperor and the Roman Army
Korneel van Lommel, The Terminology of the Medical Discharge and an Identity Shift among the Roman Disabled Veterans