Birmingham City have pulled out of Sunday's Women's Super League fixture at Tottenham because of a shortage of available players due to injury.
The club said the Football Association had denied their request to postpone.
A Birmingham statement cited "unprecedented shortage of player availability" after an "unfortunate and extraordinary run of injuries".
Three other top-flight matches have been postponed this weekend because of coronavirus cases at clubs.
And in the Women's Championship, the tie between Liverpool and London Bees has also been postponed because of "recent Covid-19 and injuries" in the Reds' squad.
On Friday, Birmingham manager Carla Ward said the Blues had only 10 players fit, with one positive Covid-19 result in the latest round of testing.
Birmingham added: "The club maintain the position that we would be putting our players at risk of further injury and jeopardise their wellbeing in pursuit of fixture fulfilment. This is not a concession we are willing to make.
"The club will liaise with the FA and Tottenham Hotspur to come to a satisfactory conclusion for all parties involved."
The FA said it could not grant postponement "as this is an injury-related issue", adding that "the outcome of the fixture will be determined by an independent tribunal" and a decision would be made "in due course".
WSL rules on the FA website list a points deduction, a fine or a postponement as three possible options if a team cannot fulfil a fixture.
On Friday, Manchester United boss Casey Stoney apologised for giving her players permission to travel to Dubai over the festive period, calling the decision "an error of judgement".
Players from Manchester City and Arsenal also travelled to the United Arab Emirates and both sides' fixtures were called off because of positive coronavirus tests. United's game at Everton was called off because of Covid-19 cases and injuries within the hosts' squad.
Analysis - 'A very difficult week for women's football'
BBC Sport's Emma Sanders
In what has been a very difficult week for all involved in women's football, the last thing Birmingham City wanted to do was not fulfil their fixture this weekend because of injuries.
Manager Ward is desperate to sign players during the January transfer window - they brought in Veatriki Sarri from Sheffield United earlier this week - but Birmingham have been struggling to name a fully fit squad for most of the season.
Ward was hopeful of two late fitness tests being passed, which would have taken their squad up from 10 players to 12, but that has not happened.
The club felt their request for the match to be postponed held weight because they had received a positive coronavirus test result.
The FA feels Birmingham's situation is an isolated one - that it is down to injuries and not related to coronavirus - but there is some frustration from Birmingham after Everton's match with Manchester United was called off because of a mixture of injuries and coronavirus infections.
In a statement, Everton said five players had tested positive for Covid-19, returned to training and were then "unable to be passed fit" by medical staff on Friday morning.
The FA has had to make some tough decisions this week but it is believed a lack of transparency and clarity in some cases has frustrated players and staff.
- Stream eight live FA Cup third-round games this weekend on BBC iPlayer, the BBC Sport website and app. Find out more here.