The military declined to identify the soldier or precisely what was written, but a source said the non- commissioned member from Quebec, made an "inappropriate statement" on Facebook about India-born Sajjan's "ethnic background", The Globe and Mail reported.
Sajjan immigrated to Canada from India when he was a young boy.
The offensive post, which was written in French, was quickly removed.
A Forces spokesman said the army's chain of command is probing the matter.
More From This Section
The incident of disrespect to the minister prompted Chief Warrant Officer Kevin West to send an e-mail to soldiers warning against such conduct, the newspaper said.
He lamented the fact a high-ranking member of the Forces made "negative" comments about the minister and warned them against disrespectful behaviour, adding that to say he is angry would be an understatement.
The Forces issued a strong statement Wednesday condemning the behaviour.
"Racist attitudes are not compatible with military ethos and with effective military service. Any conduct that reflects such attitudes will not be tolerated," he said.
"The institution is entirely committed to the principle of equality of all people and the dignity and worth of every human being," the Forces spokesman said.
"As previously stated by Chief of the Defence Staff Jonathan Vance, bullies have no place in the organisation.