Ms O’Neill said modelling presented to Stormont ministers suggests that in a worst-case scenario, the region could be facing 30,000 cases a day.
Executive ministers are involved in ongoing discussions about the situation ahead of a formal meeting on Wednesday, when it is expected new restrictions to be applied after Christmas will be announced.
But Ms O’Neill told the BBC Sunday Politics programme that ministers will act before then if it is deemed necessary.
By the end of the year this is going to be the dominant strain, this will be overwhelming and we are going to have to intervene
She said: “We are continuing to work around the clock with public health officials to understand the impact because there are things that we currently know, but there are also things that we do not know.
“In terms of what we know, we know that this is going to hit us like a ton of bricks.
“We know that by the end of the year this will be the dominant strain of Covid we know that we will peak in the middle of January, we know it is going to spread rapidly.
“What we don’t yet know is the impact in terms of our hospital situation, and we expect to understand that a bit more tomorrow and that is when we will engage again.
“Then we decide when to intervene and what is the appropriate intervention.”
Ms O’Neill also said the Stormont Executive cannot be “held to ransom” by what is happening in England in order to get financial support from the UK Government to introduce Covid restrictions.
She said: “We have been very much focused on raising finances, we need money in order to support interventions because health are telling us that the booster programme in itself isn’t enough, we are going to need an intervention of some sort.
“We need to have the backs of the workers, we need to support businesses if we have to intervene. You cannot do this without money.
“I myself have constantly engaged with the Treasury making the case for finances.
“We shouldn’t have to wait for what is happening in England in order for us to act.
“These figures are really alarming. It is going to be the sheer volume of cases that is going to be a dominant feature throughout January.
“We know that by Christmas Day we could potentially have 11,000 cases a day.
“We know that in the worst-case scenario, in terms of some of the modelling that has been done, we could be facing up to 30,000 cases a day.
“By the end of the year this is going to be the dominant strain, this will be overwhelming and we are going to have to intervene.”
She said the Executive will look at “all options” in terms of introducing new Covid restrictions.
“Everything is on the table,” Ms O’Neill said. “We have to look at all options.
“I think we will have a clearer picture tomorrow in terms of impact on hospital numbers, which is a crucially important factor in terms of any intervention that we may decide to make.
“The nature of that intervention, the timing of that intervention and the length of that intervention is yet to be decided upon.
“Wednesday is our scheduled Executive meeting but if we need to come to a decision point before that then that is certainly what we will do.”