Celtic will begin their Europa League group stage campaign on Thursday September 18, having failed earlier this week to qualify for the Champions League.
The game could take many away from answering "Should Scotland be an independent country?" for several hours that evening.
Group matches in the Europa League typically kick-off at 6pm and 8pm on Thursday evenings.
Celtic will find out on Friday who they face in the Europa League. If' it's a home tie on September 18, the club would expect to fill Celtic Park with 60,000 fans and the match is also almost certain to be televised.
A Better Together spokesman said: "This is the biggest decision we will ever take in Scotland's history, so it's vital that Celtic fans going to the game also make sure they cast their vote to keep Scotland in the UK on September 18."
A Yes Scotland spokesman said: "Celtic fans watching Europa League football on referendum night know as well as anyone the need to seize the opportunity of a lifetime and say Yes to independence - meaning guaranteed Champions League politics every year for Scotland."