It is understood Stormont ministers met on Tuesday morning and agreed the clarification to the regulations.
It followed calls by Church leaders across NI for the change.
The Executive had initially agreed that places of worship should close for all but weddings, civil partnerships and funerals from Friday until 11 December.
It is understood that those non-essential retail shops obliged to close later this week for the so-called circuit-breaker will be permitted to operate click-and-collect services.
The two-week lockdown was agreed by Stormont ministers last Thursday, in a bid to reduce the transmission of Covid-19 in Northern Ireland.
It is much tougher than previous periods of restrictions imposed by the executive, but schools will be allowed to stay open.
The Catholic Archbishop of Armagh and Primate of All Ireland Eamon Martin had questioned why off-licences could remain open but churches had to close.
He had urged the Executive to accept that for many people a “meaningful Christmas” is about more than shopping, eating and drinking and that spiritual preparation is essential.
Last week, the Moderator of the Presbyterian Church had described the closure of places of worship as a cause of “significant regret and concern”.
In a statement, Rt Rev Dr David Bruce said the Presbyterian Church continued to make representations regarding public worship to the Northern Ireland Executive in Belfast and to the Irish Government in Dublin.
Earlier this year, the leaders of NI’s four main Christian Churches asked parishioners to wear face coverings during services.