Land and Housing Minister Anna Tibaijuka had not shown "due diligence" when she took the money, he said.
Ms Tibaijuka, a former UN official, denies any wrongdoing.
She is a high-profile casualty in a corruption scandal that has rocked Tanzania's government and energy firms, straining relations with donors.
On 17 December, Attorney-General Frederick Werema resigned after MPs accused him of authorising the fraudulent transfer of about $120m to an energy firm.
He denied the allegation, but said he was stepping down because the controversy had "disrupted the country's political atmosphere".
Mr Kikwete, in a televised address, said the government was still investigating allegations of impropriety against Energy and Minerals Minister Sospeter Muhongo and his permanent secretary Eliakim Maswi.
The president's office later said that Mr Maswi had been suspended, pending the outcome of the probe.
Ms Tibaijuka rejected parliament's call for her resignation, saying the $1m was a donation for a school where she serves as the main fundraiser.
She accepted it in good faith and presented it to the school, she said.
However, Mr  Kikwete said he had dismissed her because "one of the biggest questions raised is why this money was not paid directly to the school and was instead deposited in a personal bank account in her name," Reuters news agency quotes him as saying.
Ms Tibaijuka was the executive director of the United Nations Human Settlements Programme, before she became an MP and government minister in 2010.
Tanzania's parliament, which is dominated by the ruling Chama Cha Mapinduzi (CCM) party, has been putting pressure on Mr Kikwete to sack top officials accused of siphoning government money in collusion with businessmen linked to the energy sector.
An investigation by a parliamentary watchdog committee found that about $120m had been taken from an escrow account, paid to an energy firm and then given to various government ministers.
A group of 12 donors - including Japan, the UK, the World Bank and the African Development Bank - decided in October to withhold about $490m until the government took action over the alleged corruption.
Mr Kikwete took office in 2005 with a promise to tackle corruption in government.
Tanzania's President Jakaya Kikwete has fired a senior government minister accused of wrongly taking $1m (Â£640,000) from a businessman.