Sir Brendan Barber said that employers should think about introducing flexible working hours on big-match days, or even to allow workers to watch the games on television or online from their desks.
Introducing these measures before the time would prevent disputes, as well as ensuring that employers to not run short of staff, he said.
Fixtures that could cause tension between staff and their bosses include England and Wales’ Group B clash at 2pm on Thursday June 16.
Northern Ireland is also scheduled to play two 5pm weekday matches in Group C, while the Republic of Ireland have a 5pm weekday fixture against Sweden in Group E.
Only one of the last 16 matches will take place during weekday office hours, while all the matches in the quarter finals and onwards kick off at 8pm.
“The Euro 2016 tournament is an exciting event for many football fans but staff should avoid getting a red card for unreasonable demands or behaviour in the workplace during this period,” said Sir Brendan.
“Many businesses need to maintain a certain staffing level in order to survive.
“Employers should have a set of simple workplace agreements in place before kick-off to help ensure their businesses remain productive whilst keeping staff happy too.
“Our guidance, published today, can help managers get the best from their team players, arrange appropriate substitutions if necessary and avoid unnecessary penalties or unplanned send-offs.”
Companies should also reiterate clearly their policy on the use of social media at work.
“If employers are monitoring internet usage then the law requires them to make it clear that it is happening to all employees,” it said.
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