Manager Ryan Giggs will not be involved in Wales’ three matches in November, with assistant Robert Page taking charge of the team.
The 46-year-old was arrested on suspicion of assaulting his girlfriend, several newspapers have reported.
Giggs has denied an allegation of assault made against him.
Wales have a friendly against the USA at Swansea’s Liberty Stadium on 12 November.
They then host the Republic of Ireland at the Cardiff City Stadium on 15 November in the first of two Nations League games, with Finland visiting the Welsh capital on 18 November.
Giggs’ representatives said he denies all allegations of assault made against him and is co-operating with the police.