De Gea's position at Old Trafford has come under increased scrutiny after making a mistake during the 1-1 draw with Tottenham on Friday.
His struggles have been magnified further by Henderson's impressive performances on loan at Sheffield United, who have the second-best defensive record in the Premier League.
"It's a different job to be playing for Sheffield United and for Manchester United," Solskjaer said on Tuesday.
"The two years he [Henderson] has had [at Sheffield United] have been fantastic development. He's played with and against men, played in the Championship and plays in a team that plays exciting football and the stats show he's proved worthy of a few points.
"He's learning all the time, he's a passionate keeper, developing, good coaching. One day he'll be England No.1 and United No. 1 and he needs to keep developing."
Gary Neville has also said the 29-year-old's form is "a worry" but on Tuesday, Solskjaer launched a strong defence of his goalkeeper.
"David is the best goalkeeper in the world," Solskjaer said.
"He's conceded two goals in the last seven he's played for us. He makes great saves, wins games for us and he's still the best goalkeeper in the world.
"David is working really hard, he isn't making errors you see time and time again. I'm pleased with his work.
"He's had some fantastic seasons and I don't think it's a bad run if you concede two goals in seven games. He's made matchwinning saves, he saved a point for us against Tottenham with a save."
Henderson will be ineligible for Sheffield United's trip to Old Trafford on Wednesday but Solskjaer says he expects the 23-year-old's loan deal to be extended to cover the remainder of the season.
"I would think so," he said.
"Dean's had a fantastic season again as he had last year with Sheffield United and so far he's proven the loan has worked out as we wanted."
Meanwhile, midfielder Scott McTominay has signed a new contract at the club until 2025, it was announced on Tuesday.
The deal includes an optional year's extension and the academy product said: "Whilst I understand that we all have so many other things to think about at the moment, I'm so happy to sign this contract and play a part in the future ahead for this team.
"All I have ever known is United and I hope that my passion for the club shows every time I go onto the pitch. I'll continue to give everything for this club whenever I pull on the shirt. I want to thank the manager for the faith he has shown in me and everyone at the club that has helped me to get where I am today. I'm looking forward to finishing this season on a high and hopefully achieving our aims."
McTominay has been at United since 2012 and after making his debut against Arsenal in 2017, has gone on to make 75 appearances for the club, scoring six goals.