Rob Wilson, the Conservative MP for Reading East, contacted the commission last month claiming the trust had used the social media platform Twitter to endorse the Labour Party.
Wilson said the charity had done this by "associating itself closely with, to the extent of providing its endorsement and support to, the Labour Party’s online campaigning".
He said the charity had used hashtags on its official Twitter account, including #childcarecrisis and #childcarecrunch, which Wilson said had been used and promoted by the Labour Party on the online platform.
He said the phrase "childcare crunch" had been used by the Labour leader Ed Miliband as the slogan of a campaign on growing childcare costs and was the title of a comment piece for the Fabian Society by Lucy Powell, the shadow minister for childcare and children.
Wilson also pointed out that Anand Shukla, the trust’s chief executive, is a former parliamentary and local council candidate for the Labour Party.
In a letter written to Wilson this week, the regulator said "it was unclear whether the charity had acted contrary to its guidance on campaigning and political activity" but it was "possible that public perceptions of its independence could have been adversely affected".
The commission said it had contacted the charity’s trustees to provide regulatory advice on the need to maintain independence and manage public perceptions of this.
Wilson said he had asked the commission to show him the guidance that was sent to the trust because its existing guidance predated the widespread use of social media by charities. "I am concerned that other charities might be in danger of straying into conducting inappropriate political activity," he said.
Shukla said he had received a letter from the commission and was preparing a response. "We are confident that the Charity Commission will find that the Family and Childcare Trust has fully complied with its guidelines," he said.