Police were called to an address in Worsley, Salford following reports of a disturbance. A 46-year-old man was arrested and then released on bail pending further inquiries.
A spokesperson for Greater Manchester Police said: "Police were called at 10.05pm on Sunday to reports of a disturbance.
"A woman in her 30s sustained minor injuries but did not require any treatment.
"A 46-year-old man was arrested on suspicion of section 47 assault and section 39 common assault."
A representative for Giggs, who spent his entire playing career with Manchester United and is now in charge of Wales' national team, released a statement that read: "Mr Giggs denies all allegations of assault made against him. He is cooperating with the police and will continue to assist them with their ongoing investigations."
Ryan Giggs will not have any involvement in Wales' three November matches after the manager was arrested following an assault allegation.
The Football Association of Wales (FAW) said Giggs, who denies any wrongdoing, agreed to step aside temporarily and allow Robert Page to take charge of the team.
Giggs won 13 Premier League titles and the Champions League twice during a hugely successful career with United before announcing his retirement in May 2014.
He was named Wales manager in January 2018, taking over the job following the departure of Chris Coleman.