She was detained after returning to the UK.
Photos have emerged showing her with bandages around her face, near police vans at the airport.
The PA news agency understands Ms Price, who was born in Brighton but lives in Surrey, was bailed by an out-of-hours magistrate later on Thursday evening.
She was declared bankrupt in November 2019 and again in March this year.
At a hearing in February, she was ordered to pay 40% of her monthly income from the website OnlyFans for the next three years, in relation to her first bankruptcy.
She was declared bankrupt for a second time in March because of an unpaid tax bill of more than £750,000.
