He suffered a transient ischaemic attack in his home town of Dundee on Monday and has been receiving treatment at Ninewells Hospital.
The 49-year-old MP for Dundee East is married to Shona Robison, the Scottish Health Minister, and they have a daughter at primary school in the city.
An SNP spokesman said: “Stewart Hosie had a mini-stroke on Monday afternoon - he is expected to make a complete recovery, and is hoping to leave hospital very soon."
MSPs claimed more than £12.8 million in expenses, up 8.2% on the previous year due to winding-up expenses claimed by politicians who either stood down or were not returned to the Scottish Parliament at the 2011 elections.
Excluding these costs, the total expenses paid out to MSPs was just over £11.3m, which represents a decrease of more than £500,000 on the previous year. Winding-up expenses included staff salary costs, staff redundancy and office and accommodation costs.