"She is in custody for questioning because of the communication she had with one of the female terrorists killed" in Sunday's attack, the source said, requesting anonymity. The assailants were alleged to be "sympathisers" of the Islamic State group.
The arrested woman is the widow of Aboud Rogo Mohammed, an imam killed in Mombasa in August 2012 who was until his death the main preacher at the city's Musa mosque, seen as the heart of radical Islam in Kenya.
The new arrest brings to four the number of women detained over the weekend attack. Three Somali refugees suspected of sheltering the assailants, who were arrested on Sunday, appeared before a judge today.
The three women were brought into court to be charged but police said one of them, Shukri Haji, who is said to be deaf, claimed she could not understand what the sign language interpreter was saying.
Resident magistrate Emmanuel Mutunga ordered the three be detained five more days.
The so-called Islamic State group said its "supporters" carried it out, according to the SITE Intelligence Group, quoting the group's Amaq news agency.
"The executors of the attack on the Kenyan police in the port city of Mombasa are supporters of the Islamic State and they carried out the operation in response to calls to target the Crusader states," the agency said.
Police have said two of the women involved in the knife and firebomb assault were Kenyans and that one was wearing a suicide vest that did not detonate.
Kenya's Muslim minority is largely concentrated along the Indian Ocean coast and the country in the past has repeatedly come under attack by the Somalia-based Shabaab.
Somali-led insurgents have staged repeated attacks in Kenya, including the killing of at least 67 people at Nairobi's Westgate Mall in 2013 and the massacre of 148 people at a university in Garissa in April 2015.
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