Giggs, 48, faced charges of causing actual bodily harm to Kate Greville along with controlling and coercive behaviour. He also faced a charge of common assault of Greville's sister Emma.
The jury of seven women and four men told the judge they had been unable to reach verdicts after a trial which had lasted over three weeks.
The Crown Prosecution Service now has seven days to decide whether to proceed with a retrial.
Giggs, the former Wales manager, had pleaded not guilty to the charges and his defence said the allegations were "based on distortion, exaggeration and lies".
The former United player was first arrested in the case and released on bail in November 2020.