Buccaneers and Tullamore have also had to cease playing matches.
Ireland head coach Andy Farrell says his side would "happily" accept the postponement of their upcoming test matches if needed, but is hopeful they can resume their 6 Nations campaign without issue.
Ireland restart their 6 Nations campaign next week against Italy at the Aviva Stadium, before travelling to France the following week.
However, those games could be scrapped if Ireland were to move into level-5 Covid restrictions.
If that were to happen, Farrell says rugby would be the least of their concerns.
Meanwhile, the IRFU have suspended the Energia Community Series which both Buccaneers and Tullamore have been taking part in.
Buccaneers are in 3rd place in the Connacht conference having won one and lost two from their three games.
Tullamore lie in 8th in Leinster conference second tier.
They've picked up one draw and two defeats since the resumption of the sport.
In a statement to clubs, the IRFU has reminded them that in level three and four restrictions teams are limited to non-contact training of up to 15 players.
Third Time The Charm As Laois Claim Joe McDonagh Cup
Offaly Pupils Become Local Stars After Publishing Bestselling Book
Katie Taylor To Fight At Croke Park In September
Laois And Westmeath Set For Big Tests In Intermediate Camogie Championship
I Knew I Had To Play A Good Round To Win - Ella Cantwell
Mullingar Athletic And Clonaslee United To Clash In Combined Counties Cup Final
Shane Lowry And Rory McIlroy In Contention At Memorial Tournament
There's Serious Competition In The Laois Panel - Mark Dowling
Westmeath Ladies Look To Book All-Ireland Quarter-Final Spot
Alex Dunne Aiming For Big Weekend In Monaco
Offaly Camogie Captain Looking Forward To Kilkenny Clash
Shane Lowry In Action At Memorial Tournament
Laois Aiming To Make It Third Time Lucky In Joe McDonagh Cup Decider
Galway To Host Westmeath On Sunday June 14th
Second Round Draw Made For FAI Cup
Cian Reddy Keeps Up Unbeaten Professional Record
Westmeath Ladies Get Opening Win In All-Ireland Intermediate Championship
Athlone Town Knocked Out Of All-Island Cup
Limerick See Off Offaly In Senior Camogie Championship
Athlone Town Suffer Defeat Away To UCD In First Division