Ben Judd from St Ives had been pencilled in to officiate the SWPL division one west match at Trungle Parc, but failed to arrive, and with no time to find a replacement, the game was abandoned.
League secretary Phil Hiscox said it was 'with relutance' that he had ordered the replay to take place on Easter Monday, April 21.
He added that the league were investigating the reasons why no referee had been present at Trungle Parc.
In a statement, Hiscox said: "The circumstances involving why no referee was present are being investigated and until I have had the thoughts of the appointers and the referee in question I am not able to comment further on how or why this has happened.
"However the game must be played and Mousehole still have nine games to play and Vospers Oak Villa eight games."
He added: "There are no Saturdays where either team is spare, and without lights it is not practical to play it on a midweek. I am not authorised to order the game to be played on a Sunday (clubs can only mutually agree that). May Day Monday already has both clubs playing league games and extending the season is neither practical (FA Cup final day) nor is it fair on other clubs trying to secure the West title alongside Mousehole.
"Therefore with reluctance, but with firm insistence, I order under league rules that the game be re-arranged for Monday, April 21, 3pm at Trungle Parc, Mousehole.
"Both teams are so instructed under rule to play that day, failure to do so will result in penalties for failing to fulfil a fixture as per league rules.
"I am fully aware that Easter Monday is also in Cornwall the day of the County Cup finals. I am not making this order lightly and in 7 years since the SWP was formed I have always found a way of avoiding games taking place in Cornwall that day.
"However the unusual lateness of todays postponement, the sheer number of games this winter has thrown up to be fitted into other dates and the circumstances of the travel between the two clubs means I must make such an order."