The pop star was given the night's top honour for her multi-million selling record 25, but told the audience, "I can't possibly accept this award".
"I'm very humbled and I'm very grateful, but Beyonce is the artist of my life".
The British singer then appeared to break the award in two accidentally and offer a piece to her fellow nominee.
Adele's victory over Beyonce is certain to boost complaints that the Grammys habitually overlook black artists.
Several artists, including Frank Ocean and Kanye West, chose to skip this year's ceremony on that basis.
Ocean even declined to submit his critically-acclaimed album, Blonde, for consideration, saying the Grammys did not "seem to be representing very well for people who come from where I come from, and hold down what I hold down".
Two years ago, West rushed onto the stage in protest when Beck's Morning Phase beat Beyonce's last LP in the best album race.
However, Adele's 25 was by far the biggest-seller on this year's shortlist; outselling Beyonce's Lemonade by a factor of 10 to 1.
It is unclear if Adele will officially reject her award. If she does, it would only be the second time in history that has happened.
The last was in 1990, when Sinead O'Connor turned down best alternative album for  I Do Not Want What I Have Not Got, claiming the ceremony was too "commercialised".
Main winners
Whatever the outcome, Adele remains one of the night's biggest winners.
She won five prizes in all, including three of the top four: Best album, song of the year and record of the year - the latter two both rewarding her 2015 comeback single, Hello.
Chicago's Chance the Rapper also took three prizes, including best rap album for his self-released record Coloring Book.
"I know people think independence means you do it by yourself, but independence means freedom," he said as he picked up best new act at the start of the ceremony.
Rock icon David Bowie won in each of the five categories he was nominated for, including best alternative album, for Blackstar, and best rock performance, for the album's title track.
And Beyonce wasn't left completely empty-handed: she took home best urban contemporary album and best music video, for the politically-charged Formation.
The star, who is pregnant with twins, also gave an ambitious and logistically complex performance of the songs Love Drought and Sandcastles, themed around the ideas of rebirth, regeneration and healing.
Dressed in flowing, golden Egyptian robes and an elaborate headdress, she dedicated the performance to motherhood, proudly displaying her baby bump as she sang.
But while Beyonce's performance was flawless, others were marred by technical issues.
Lady Gaga duetted with Metallica on the song Moth to the Flame, but singer James Hetfield was inaudible throughout the first verse.
He later sang cheek-to-cheek with Gaga, sharing her microphone, but angrily threw his guitar to one of his roadies at the end of the performance.
Adele also went off-key during a tribute to George Michael, and tearfully asked if the song could be started again. It was, and she received a standing ovation for her troubles.
Respects were paid to Sir George Martin, Leonard Cohen and other musicians we lost in 2016, while Bruno Mars honoured Prince by playing the star's trademark cloud guitar in a pitch-perfect rendition of Let's Go Crazy.
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Adele has apparently turned down the Grammy award for best album, saying Beyonce deserved it more.