Normality will not return for at least six months in Ireland, the Taoiseach said.
It could be May or June before mass vaccination brings about significant change, Micheal Martin added.
By the end of January the health system should be delivering three vaccines.
Mr Martin said: "The first six months of 2021 we will see improvements, but we certainly not will see normality in the first six months."
The European Union approved the Pfizer-BioNTech vaccine in December.
The European Medicines Agency issued a provisional marketing authorisation.
Nursing home residents are among the priority groups.
Mr Martin said that initial phase would make a "significant difference" and protect the most vulnerable.
He added: "Certainly manufacturing of the vaccine will be ramped up, certainly from March onwards."
Mr Martin said May and June had been identified as "critical" months.
He said December's concerns over the emergence of the mutant strain of Covid-19 in parts of England had highlighted continued uncertainty.
The Taoiseach expressed confidence in vaccine supplies in the long term.
"By the end of January you will have three vaccines and what I am saying is conservative.
"I can also see a scenario where manufacturing ramps up more quickly and where higher volumes of vaccines goes to member states more quickly, that is a more hopeful scenario."
The State entered its third lockdown on Christmas Eve as a range of restrictions were introduced.
Bars, restaurants, hairdressers and beauty salons shut in a bid to stifle the spread of coronavirus.
Tanaiste Leo Varadkar warned people to expect the restrictions, which are subject to review, to last until early March.
Mr Martin acknowledged the future was uncertain.
"We can impact the virus as people, we can keep the pressure on it by reducing contacts."
Under the fresh restrictions, retailers will be permitted to remain open, though they will be urged not to hold post-Christmas or January sales to keep numbers in store low.
Gyms, leisure centres and swimming pools will remain open. Outdoor training can continue.
No sports matches can take place, apart from those at elite level.
Travel between counties will be banned from St Stephen's Day.