Matthews won the green jersey last year and had looked in decent form as he finished seventh on the opening stage before leading the team across the line as they took fifth place in the team time trial on stage three.
The Australian rider would have been among the favourites to take victories on stages five and six, with Wednesday's stage featuring a lumpy parcours ahead of a technical finish in Quimper, before Thursday sees an uphill finish on the Mûr de Bretagne.
However Matthews was ill overnight, waking up vomiting and with a fever, and struggling to eat ahead of the stage, with the team taking the decision to pull him out of the race.
Sports director Luke Roberts explained the disappointment for Matthews in having to abandon the race, and how he would also be missed by the team in supporting Tom Dumoulin's general classification ambitions.
However he also said how the team had acted quickly on Matthews's illness, isolating him from his team-mates to prevent the illness from spreading through the team.
Watch: Tour de France stage four highlights
"We're very disappointed and today would have been a highlight for him. It's a stage that's very well suited to him and he could have got a good result," Roberts said ahead of the start of stage five.
"Tomorrow would also have been suited to him and he also brings a lot to the team in regards to helping Dumoulin target the general classification. He will be a big loss."
"No other riders have shown any symptoms. Michael has been isolated all morning so in the case it is a virus, as we expect it is, we hope that we have caught it early enough that other riders will not be affected.
Matthews also spoke of his disappointment of having to abandon the race, but said that it would have been impossible to continue with his illness.
"I'm really disappointed to not start this morning. I've been really ill this morning and tried all I could to make it to the start line, but feeling like this, it's simply not possible," Matthews explained. "I will now go home to recover and will continue cheering for the guys from there.
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Henry Robertshaw began his time at Cycling Weekly working with the tech team, writing reviews, buying guides and appearing in videos advising on how to dress for the seasons. He later moved over to the news team, where his work focused on the professional peloton as well as legislation and provision for cycling. He's since moved his career in a new direction, with a role at the Department for Environment, Food and Rural Affairs.
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