Lindstrom was hurt when he stepped awkwardly while fielding a bunt during the ninth inning of Monday's game at Kansas City. He left the game immediately and was placed on the 15-day disabled list Tuesday with a dislocated ankle tendon.
"I know he's going to be down for a while," Ventura said.
Lindstrom will undergo surgery Friday with the recovery time projected around three months, meaning he likely will not return before late August.
"They'll try to fix it and get him back, but right now we're just hoping everything goes well for him and he can get back as soon as he can," Ventura said.
Ventura said right-hander Ronald Belisario, who got a chance to close Tuesday's game, recording his first save of the season while giving up a run, would be his closer.
The Associated Press contributed to this report.