Mr Mutunga said he had received a “poison-pen letter” from an outlawed group “extolling” violence.
On Friday, the High Court ruled that it did not have the power to annul Mr Kenyatta’s candidacy.
He is due to be tried at The Hague for crimes against humanity.
The case at the International Criminal Court (ICC) stems from allegations that Mr Kenyatta fuelled violence that followed the disputed 2007 presidential election.
He and his running mate William Ruto are due to be tried at The Hague about a month after the 4 March election.
Kenyan pressure groups asked the High Court to disqualify them from contesting the election because of the ICC case.
But the High Court refused.
More than 1,000 people died in the violence which swept through Kenya after the 2007 election.
The violence ended after a coalition government was formed.
Mr Kenyatta and Prime Minister Raila Odinga are the frontrunners in next month’s election.
President Mwai Kibaki is stepping down after two terms in office.
Mr Mutunga said he had received the “poison-pen letter from the Mungiki Veterans Group/Kenya Sovereignty Defence Squad”, a banned group which was heavily involved in violence after the 2007 poll.
“It warns against an adversarial ruling on the presidential and deputy presidential candidacy of Uhuru Kenyatta and William Ruto,” Mr Mutunga said, at a news conference in Nairobi.
“The letter extols the violent ‘exploits’ of the Mungiki movement and threatens dire consequences.”
‘Cabal of retrogrades’
Mr Mutunga said five judges had been attacked ahead of the elections.
He also faced an illegal attempt by an immigration officer at the airport in Nairobi last week to block him from flying to neighbouring Tanzania, he said.
“It requires some courage, ignorance, or political patronage or a combination of all three to stop a chief justice from travelling,” Mr Mutunga added.
Intelligence chief Maj-Gen Michael Gichangi later phoned to apologise for what he called a “small hiccup”, Mr Mutunga said.
“It has never happened on any of my numerous previous trips,” he said.
“I have, therefore, concluded that this is deliberate harassment… I am convinced it is political.”
Mr Mutunga said judges would not be held hostage by a “cabal of retrogrades”.
“We shall decide all cases independently and with scrupulous fidelity to the constitution,” he added.
“Let no individual, group, candidate, or supporter imagine that cowardly and darkly acts such as these will cow us.”