The regulator said it had visited the charity earlier this month following a complaint and had contacted trustees again on Monday after a Sunday Times story yesterday about Davidson’s salary.
The newspaper reported that Davidson said that if he hit fundraising targets, he was able to draw a salary of £43,000 a year from the charity, which he helped set up, and also claimed £11,000 in expenses.
It is not clear from the news story when or where Davidson had made the alleged comments.
That charity was set up in 2014 to support veterans suffering from mental health and addiction issues or who were in prison. It had an income of £252,200 and spent £229,100 in the year to 31 October 2015, according to accounts filed with the Charity Commission.
It was awarded £1m in 2015 from the Armed Forces Covenant Fund, which allocates the money paid in fines by banks involved in the Libor scandal to military charities.
"I work full-time at it [the charity] and I have to raise between four and five times that much money before I get paid a penny of it," Davidson reportedly said.
A commission spokesman said: "The Charity Commission received a complaint regarding the charity’s governance and visited the charity earlier this month.
"The commission is assessing the information provided by the charity to determine whether there are any regulatory concerns in relation to the remuneration of one of the charity’s trustees and will today contact the trustees for further information."
Last week the Sunday Times ran a story questioning the use of Libor funds on three veterans charities, claiming the money was being spent on ineffective treatments.
Care After Combat was not among the three charities named in the story, but in a statement on the charity’s website, Davidson said that the charity had responded to the story by sending its first annual review to the editors of all national newspapers to let them know the charity was doing "very well, thank you".
The singer Katherine Jenkins and Falklands War veteran Simon Weston are also trustees of the charity.
Care After Combat and Jim Davidson did not respond to Third Sector’s request for comment.