The singer said she was “devastated” to let fans down after taking medical advice.
Taking to Twitter to break the news, the ‘Hello’ singer said: “To say I’m heartbroken would be a complete understatement.”
The 29-year-old had already played two sold out shows at the London venue on Wednesday and Thursday night, and was due to perform again on Saturday and Sunday evening.
In a lengthy statement posted on Twitter, Adele explained that she had struggled vocally during the first two nights of her Wembley residency.
“I had to push a lot harder than I normally do,” she writes. “It turns out I have damaged my vocal cords. On medical advice, I am simply unable to perform over the weekend.
“I’ve considered doing Saturday night’s show, but it’s highly unlikely I’d even make it through the set and I simply can’t crumble in front of you all and walk out on you in that way.”
She added that she was so desperate to be with her fans that she had even considered miming.
“But I’ve never done it and I cannot in a million years do that to you. It wouldn’t be the real me up there,” she says.
“I’m sorry for your disappointment... You know I would not make this decision lightly.”
She concluded by saying refunds would be available if the shows could not be rescheduled.
“There will be more information over the next few days. I’m sorry, I’m devastated... please forgive me x.”
Earlier this week the singer gave her strongest signal yet that she won’t be touring again following her final London shows.
She delivered the news to fans in a handwritten note buried inside her tour programme.
She wrote: “Touring is a peculiar thing, it doesn’t suit me particularly well. I’m a real homebody and I get so much joy in the small things. Plus, I’m dramatic and have a terrible history of touring. Until now that is!
“I’ve done 119 shows and these last four will take me up to 123, it has been hard but an absolute thrill and pleasure.
“I only ever did this tour for you and to hopefully have an impact on you the way that some of my favourite artists have had on me live.
“And I wanted my final shows to be in London because I don’t know if I’ll ever tour again and so I want my last time to be at home.”