TDs and senators will be required to wear face coverings in Leinster House and the Convention Centre Dublin (CCD) where parliamentary sittings are being held.
The new rule will also apply to Oireachtas staff, political employees and the media.
In an email to TDs and senators, Ceann Comhairle Sean O Fearghail said wearing face coverings can play an important part in addressing the spread of the virus in indoor settings where it was not always possible to adhere to two-metre social distancing.
"Therefore, I am strongly encouraging members to wear a face covering in shared spaces and circulation areas, where at all possible, with effect from Monday, July 20," he said.
"I would also encourage members to wear face coverings in the chamber and in committee rooms, when not speaking or making a contribution.
Members are requested to use their own face coverings but the facilities unit will have reusable and disposable masks available if required, he added.
Mr O Fearghail said Leinster House was a shared workspace and it was in everyone's interest that those working there "adopt a consistent and safe approach" to returning to work during the Covid-19 pandemic.