Red Devils captain Maguire has come under huge pressure for his early season performances, and was targeted with brutal criticism after below-par displays against Liverpool and Manchester City.
Getting a brief respite from his poor club form, Maguire scored England's first goal in a 5-0 win against Albania during the international break, cupping his ears to the crowd.
Keane commented on the gesture, saying: "He obviously puts his hands like he's shutting the critics up, but I think that's embarrassing.
"He's been a disgrace the last few months for Manchester United and he thinks scores and it's going to shut his critics up. Embarrassing."
Despite fellow pundits Ian Wright and Jermaine Defoe agreeing with Keane's assessment on the day, Magurie - who was also backed by England boss Gareth Southgate - offered a measured response post-match.
"I'm Manchester United captain," he said. "Of course I'm going to get criticism when the team isn't doing well but the celebration wasn't directed at anyone."
Maguire's manager Solskjaer has benefited from the support of his ex-United teammates in the media, with the likes of Keane, Gary Neville and Rio Ferdinand regularly defending the Norwegian.
Pressure has ramped up this season though, with Solskjaer the favourite to become the next Premier League manager to lose their job, and his friends in the media have begun changing their tune.
Ferdinand recently said it may be time for the baton to be passed by Solskjaer, while Keane admitted he no longer has belief in the manager.
And Solskjaer couldn't resist making a sly dig at his and the team's critics whilst defending Maguire ahead of their return to Premier League action against Watford on Saturday.
"As a team we've not performed at the standard we know that we can do and at the levels we need to be at," Solskjaer said.
"Harry [Maguire], as Gareth [Southgate] rightly said, he's not one to hide on the treatment table or try to find any excuse to sit out games.
"Harry is a top professional who wants to be there for the manager every single time and he trains really well and I think this week going away and scoring a couple of goals for his country will help his form and confidence.
"For me, no I've not considered taking away any captain's armband away from him. He's been an absolute stalwart for us on and off the pitch since he came in.
"The so-called experts have their opinions and that's their job to put their opinion that's not something we have to worry too much about.
"As a true example of a Man United player Harry is always there for his team and his country."
The 'so-called experts' comment can clearly read as a reference to Keane, and the rest of those now turning on the boss, but could there have been another dig aimed at his former teammate?
Solskjaer's final quote that Maguire is 'always there for his team' could well be perceived as being aimed Keane, who famously being sent home from Ireland's 2002 World Cup squad following his public spat with former manager Mick McCarthy.
If you're unfamiliar with that story, here's how it was described by former Republic of Ireland international Clinton Morrison on talkSPORT: "Roy was steaming!
"Roy was always ready to blow back then, always fighting things and always ready to go into one.
"They got separated and Roy stood there and said: 'Go on, Mick. What are you going to do? Make a decision.' So he had to send him home.
"And, literally within two days, he was back in Manchester wearing that horrendous Diadora tracksuit he used to wear walking his dog.
"I couldn't believe it!"