First-year coach Mike Johnston said both players were injured in the lead-up to camp, which begins Friday.
Neither injury is considered long term. Johnston added Crosby's issue is not related to a wrist injury that hindered him late last season and into the Stanley Cup playoffs.
"We'll see over the next few days, I don't expect any of them to be long," Johnston said. "But when the trainers and the doctors inform us at this time of the year that we better be cautious with a few people, then we're going to be cautious. ... These are injuries that have taken place in the short term. I haven't watched the skates since they've been here, when they've been out on the ice skating, but it's been in the last four to five days."
While there is no timetable for either player's return, Johnston added he expects it to be "fairly short."
Johnston said he doesn't mind dealing with minor injuries at this time of the year, as they are a result of the players pushing themselves for the start of the season.
"The issue is, I think that sometimes the guys, when they get in here together, they get training together, they get on the ice together. It's run by the players, so it's controlled to a degree, but I think the guys, the good thing here is that they're training hard," he said. "They wanted to push each other on the ice. They wanted to push each other off the ice. They're together, which is really good to see."
While the Penguins will be without Crosby and Malkin, forward Pascal Dupuis and defenceman Olli Maatta will wear red non-contact jerseys in practice on Friday as they come back from significant injuries.
Dupuis has not played since last December, when he tore the ACL in his right knee against the Ottawa Senators. Maatta was expected to miss up to six months after undergoing shoulder surgery in May. Dupuis said he feels 100 per cent and expects to begin taking contact in about a week.
"It feels great," Dupuis said. "The timeline for recovery, the ligament just needs to heal a little more ... I have been on the ice. I have skated quite a bit, so hockey-wise I think I'm ready. They're trying to avoid me already. I'm trying to bump into them to see how it feels, so they'll see the red jersey coming up.
"If I'm wearing it, it's for a reason ... but if you asked me, I'd be wearing a black jersey and bumping into everybody."