The charity had been accused in a newspaper article of funding the Al-Ihsan Charitable Society, which was designated in the UK in June 2005 under the Terrorism (United Nations Measures) Order 2001, making it a criminal offence to fund it without a licence from HM Treasury.
The commission opened an investigation in March after it was contacted by a journalist who alleged that Muslim Aid had made payments in 2005 to two organisations linked with terrorism.
"By publishing this report, the commission has given a public assurance that public allegations of links between the charity and terrorism are unsubstantiated," says the investigation report.
The investigation found that although Muslim Aid had funded the Al-Ihsan Charitable Society, which supports older people and disabled children, in 2002 and 2003, funds worth £13,998 that it had originally put aside for the organisation in 2005 were never paid after the financial sanctions were imposed.
The commission found inconsistencies in the extent of information Muslim Aid held about different funding applications and projects.
"The charity was unable to demonstrate conclusively through its record-keeping that it had followed its own due diligence and monitored procedures consistently," the report says.
Sir Iqbal Sacranie, the chair of Muslim Aid, said he was satisfied with the conclusions.
"Muslim Aid looks forward to working with the Charity Commission to ensure that the issues that relate to the wider charity sector in the report are also fully addressed by Muslim Aid, including updating our governing document and strengthening our record-keeping and filing procedures," he said.