The England international, 27, was questioned by police on Monday following allegations reported in the British media that he engaged in sexual activity with a 15-year-old girl.
Durham Constabulary said a 27-year-old man had been released on bail "pending ongoing investigations" and will answer bail on March 18.
Johnson has been suspended by Sunderland pending the outcome of the police investigation.
Meanwhile, Durham Police issued a statement reminding members of the public that it is an offence in Britain to identify a person who may or may not be a victim of a sexual offence.
"Victims of sexual assault are guaranteed the legal right to lifetime anonymity and publishing any details, including on social media, which may lead to their identification, is contrary to the Sexual Offences (Amendment) Act 1992," a spokesman said.
"Durham Constabulary wishes to remind social media users, and anyone else, who breaks the law that they will be dealt with robustly."
Johnson, who has won 12 England caps, returned to his native northeast in 2012 when he joined Sunderland from Manchester City in a £10 million ($15 million, 13 million euros) deal.
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