Morgan, 55, probed the 53-year-old Secretary of State for Business about the government's response to the coronavirus pandemic, and their discussion quickly became tense.
Piers accused the politician of not answering him properly, and continued to fire straight to the point questions at Sharma.
When asking him about coronavirus testing, Piers spoke about the government "counting test results twice".
He then said: "Again I'll just ask you one more time, and if you don't know, just tell me you don't know.
"Do you know how many people we tested yesterday or the day before?"
Sharma answered: "Piers what I can tell you, is that there were 234,000 tests that were actually processed, and there tens of thousands of people who have of course been tested through rapid testing in Liverpool, and of course we are looking to roll that out further..."
Morgan interrupted the politician and said: "Lets move on, because the answer is you do't know."
"Well I've given you the facts", the government representative replied.
Piers raged: "No you didn't."
The pair clashed as they both began talking over one another to get their point across.
Morgan raged: "You do this a lot, with respect to you, you answer a completely different question."
"They [viewers] hear me asking you one question and you give a different answer", he added.
When talking about whether Christmas would go ahead after lockdown, Sharma said: "It's too early to talk about precisely where we might be at Christmas, but of course I want to have as normal a Christmas as possible. I want to ave members of my family around that Christmas table."
Piers said he would "rather some honestly" than "nonsense to make us feel good about Christmas".
Viewers went into meltdown during the tense interview, and a few predicted there could be another GMB "government boycott".
One said: "Omg this interview with Alok Sharma is making my toes curl. There'll be another boycott soon."
While another wrote: "What was the point in Piers Morgan b****ing about this government boycott for over 200 days if when a government minister does come on the show he just talks over them so we can't hear what they're saying anyway?"
Good Morning Britain airs weekdays at 6am on ITV.