Iker Lecuona will again be drafted in to replace him for LCR Honda at the grands prix in Malaysia and Qatar.
That will only leave one round remaining - the season-finale in Valencia.
Rins' potential participation in Valencia remains unknown.
Crucially, his ability to partake in the postseason test in Valencia - where he could jump on a Yamaha for the first time ahead of his 2024 switch - must be in doubt.
Rins is recovering from an additional surgery in the wake of the broken leg he suffered at Mugello.
He initially missed seven rounds but, despite returning, withdrew in Australia due to pain in his leg.
Rins underwent another surgery to address that pain and will remain sidelined.
His sole season at Honda saw him become the manufacturer's first grand prix winner (aside from Marc Marquez) since 2018 in Texas, before then suffering a year-altering injury.