Messina also coached the Spurs in Games 3 and 4 following the death last Wednesday of head coach Gregg Popovich's wife, Erin. She was 67 and had been battling an illness for an extended period.
The Spurs won Sunday's game 103-90 but trail the Warriors three games to one heading into Tuesday's road contest.
Messina joined the Spurs as an assistant in 2014. He won four Euroleague championships and was a two-time Euroleague coach of the year. Sources told ESPN's Adrian Wojnarowski last week that Messina is set to interview for the Charlotte Hornets head-coaching job.