Malkin, the Penguins center, and Varlamov, the Islanders goalie, each practiced Saturday but did not dress Sunday when the Islanders won 4-3 in overtime at Pittsburgh.
Makin did not participate in line rushes or power-play drills in the practice. The center missed the final 8:48 of Pittsburgh's regular-season finale May 8, when he thought he might have tweaked something.
Penguins coach Mike Sullivan did not discuss Malkin after the game.
"I think he's working through the process," Sullivan said Friday. "He's trying to capture his very best game. He's working it through it every day. He's working extremely hard at it. He's excited about the opportunity in front of us.
"'Geno' works really hard at getting back. He's an important player for us, and I think he understands that he wants to be a part of it. So he's worked extremely hard to get to this point."
Malkin had four assists in four games after he returned May 3 from a lower-body injury that forced him to miss 23 games.
Varlamov practiced after leaving New York's regular-season finale May 10 following the second period because of "a little strain," according to coach Barry Trotz. He was 19-11-4 with a 2.04 goals-against average and a .929 save percentage in 36 games (35 starts). He tied Colorado Avalanche goalie Philipp Grubauer for the NHL lead with seven shutouts.
Ilya Sorokin started and made 39 saves for the Islanders in his first game in the Stanley Cup Playoffs, with Cory Schneider as the backup.
"We had to make a decision, really, last night," Trotz said Sunday. "[Varlamov] skated both days. He's going to practice tomorrow as well. We just thought, long-term, that's one thing that we think we have is two capable goalies. If we want to have any success, we're going to need both of them. So we said, 'You know what? Let's sort of do what's right. Let's not risk anything here. Let's be cautious. We'll give him another day of practice. And then he'll be 100 percent.'"
Malkin reached 1,100 points in his NHL career with a goal and an assist in a 4-1 win against the Boston Bruins on March 15 before being injured against Boston the following day.
In his 15th NHL season, Malkin scored 28 points (eight goals, 20 assists) in 33 games. The three-time Stanley Cup champion (2009, 2016, 2017) scored 12 points (four goals, eight assists) in an eight-game point streak that ended March 16. He's scored 169 points (63 goals, 106 assists) in 166 Stanley Cup Playoff games. He won the Conn Smythe Trophy voted as most valuable player in the 2009 playoffs, helping the Penguins win the Cup with 36 points (14 goals, 22 assists) in 24 games.
NHL.com deputy managing editor Brian Compton contributed to this report