Make that two significant injuries for the No. 2 pick.

On Thursday, 49ers general manager John Lynch said rookie edge rusher Nick Bosa sustained an ankle sprain in practice Wednesday that was more severe than initially reported. Lynch said Bosa had characteristics of a high ankle sprain and said his availability for the regular-season opener at Tampa Bay on Sept. 8 was in question.

Head coach Kyle Shanahan said the 49ers were “hoping” Bosa could play in Week 1. Lynch said the 49ers would be “very prudent” with Bosa.

“It’s a significant ankle sprain,” Lynch said on KNBR. “There’s that dreaded high ankle sprain. He doesn’t have a full blown one, but it has some components of that. … We won’t see him in the preseason, and we’ll go from there.”

Bosa has sustained two injuries in 12 NFL practices.

In May, in his second practice, Bosa sustained a hamstring injury that sidelined him for the rest of the offseason program. On Wednesday, in the 10th practice of training camp, Bosa was injured when he caught up in a pile on a running play.

Bosa’s brother, Joey, is a Pro Bowl pass rusher with the Chargers. His dad, John, was a defensive lineman who was a first-round pick of the Dolphins. Nick Bosa was viewed as an unusually polished draft prospect.

In fact, his injury history was easily the biggest question mark about him as a player. He played in just three games last year at Ohio State because of a core-muscle injury that required surgery. He also sustained a torn ACL as a senior in high school.

Shanahan was asked if the 49ers were concerned Bosa will have trouble staying on the field in the NFL. Shanahan noted Bosa played in 29 straight games at Ohio State before last year’s injury.

“Not with me,” Shanahan said. “I go back to his history and the guy stayed on the field throughout college. He played 12 games his freshman year. (Fourteen) his sophomore year. He played in three his next year and had a surgery. …

“Now we have a guy come in and someone landed on his leg (Wednesday). That doesn’t make me say someone is injury prone because he had a serious injury in college and he tore his ACL sometime in high school, like 60 percent of the players out there.”

Shanahan was, perhaps, purposely exaggerating, but he’s obviously overstating the rate of ACL injuries among NFL players. And he failed to mention Bosa’s hamstring injury in the spring.

However, it’s understandable Shanahan is defending a player he indicated was very upset by his latest injury. Shanahan wanted to make it clear Bosa’s injury history does not reflect a lack of toughness.

“It’s hard for me to watch because everyone acts like he’s hurt and will do stuff like this,” Shanahan said. “I’ve been around probably one of the most physical rookies in practice that I’ve been around as far as playing the run. Playing the pass. He gets after it. He’s tough as could be.

“The last thing he wants to do is get hurt. He’s trying to go out there and play with it. He wants to come back tomorrow. But he had an over-300-pound man land on his leg, and it was very fortunate that we didn’t lose him for the year.”

Of course, it’s premature to put an injury-prone label on Bosa or any NFL rookie. But the fact that he’s a No. 2 pick who has been sidelined by three injuries in the past 10-plus months means the topic won’t be tabled soon.

“We don’t feel he is injury prone,” Lynch said. “He had a core-muscle deal in his last year in college. He took that year and decided to get healthy. Yesterday, he had a large human being fall on his leg while he was engaged with someone else. So some of those you just can’t — that’s football. You can’t prevent that.”

The good news for the 49ers: Bosa had been living up to his draft status in training camp, in which he regularly enjoyed pass-rush success against Pro Bowl left tackle Joe Staley and right tackle Mike McGlinchey, the No. 9 pick in 2018.

“The great thing I can tell you about Nick Bosa is he’s been dominating practice out here on a daily basis,” Lynch said. “He’s a game-changing type player. Everything we hoped and expected.”

The 49ers had more encouraging news concerning the other significant edge rusher they added in the offseason. Lynch said Dee Ford (knee tendinitis) would return to practice in the days before the 49ers play at Kansas City on Aug. 24. The 49ers haven’t determined if Ford will play in that game.

Eric Branch is a San Francisco Chronicle staff writer. Email: ebranch@sfchronicle.com Twitter: @Eric_Branch