The Health Ministry said on Saturday that four people had tested positive for the novel coronavirus strain first detected in South Africa, with dozens of cases of the new British variant already recorded.
The infections were detected in travelers arriving from South Africa.
The two new strains are, reportedly, more infectious than previous variants of the virus.
Israel has launched a nationwide vaccination program and more than 70 percent of Israelis over the age of 60 have received the first dose, with some 1.817 million jabs already administered, according to Health Minister Yuli Edelstein.
Prime Minister Benjamin Netanyahu, who was given his second jab on Saturday, said in a brief statement on Israeli television that all Israelis could be vaccinated within two months and "no later than the end of March".
Netanyahu announced Thursday that he had signed a deal for enough doses of the Pfizer-BioNTech vaccine for all Israelis over 16 to be inoculated.
A laboratory study conducted by Pfizer said last week its vaccine appeared to work against a key mutation in the highly transmissible new variants of the coronavirus discovered in both the UK and South Africa.
The not-yet peer reviewed study by Pfizer and scientists from the University of Texas Medical Branch indicated the vaccine was effective in neutralizing virus with the so-called N501Y mutation of the spike protein.
Reuters contributed to this report