The 47-year-old former Manchester United footballer has also been charged with one count of coercive and controlling behaviour.
A statement from Greater Manchester Police (GMP) said: "A man from Salford has been charged with three offences after police were called to reports of a disturbance in the Worsley area in November 2020.
"Ryan Giggs has been charged with causing actual bodily harm to a woman in her 30s and common assault of a woman in her 20s. Both counts relate to an incident on the evening of Sunday 1 November 2020."
The GMP statement said the coercive and controlling behaviour charge against Giggs concerned the period from December 2017 to November 2020.
"He has been bailed and is due to appear at Manchester and Salford Magistrates' Court on Wednesday 28 April 2021," the force said.
"Police were called at 10.05pm on Sunday 1 November 2020 to reports of a disturbance at an address on Chatsworth Road, Worsley.
"A woman in her 30s was treated for injuries at the scene."
Giggs has denied the allegations against him.
He won 13 Premier League titles and the UEFA Champions League twice during a hugely successful career with United before announcing his playing retirement in May 2014.
He was named Wales manager in January 2018, taking over the job after the departure of Chris Coleman.
The Football Association of Wales (FAW) said Giggs would not be in charge of the team for the upcoming UEFA Euro 2020 finals in the wake of the charges.
Robert Page will serve as manager, the FAW said.
"An FAW board meeting will be convened to discuss these developments and its impact on the association and the national team," an FAW statement read.