Beyonce, who is married to rapper Jay-Z, announced her pregnancy in an Instagram photo in February - the most-liked post in history on the network.
The couple already have a daughter, Blue Ivy, aged five.
There has been no official confirmation of the birth from Beyonce and Jay-Z themselves.
In one, the 'Lemonade' singer stood naked, cradling her belly with one hand and a breast with the other, next to the sculpted head of an Egyptian ruler.
Speculation about the twins' birth had grown in recent days after a woman was photographed entering a Los Angeles hospital on Friday holding a card that read "B + J".
Beyonce is the most-nominated star in the history of the Grammy awards, and her album Lemonade was the world's best-selling record of 2016.
She had been due to headline the Coachella music festival in California in April, but pulled out on her doctor's advice.
The twins' birth - if confirmed - comes only days after actor George Clooney and his wife Amal welcomed their own set of twins, Ella and Alexander.
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