Mary Lou McDonald says the situation 'seems to be terribly inappropriate'
Ministerial positions shouldn't be handed out like baubles, according to the Sinn Féin leader.
It comes as Independent Alliance TD Sean Canney is considering his future after a row over a ministry.
When the current Government was formed, it was decided Deputy Canney and Kevin 'Boxer' Moran would split a junior ministerial position in charge of the Office of Public Works.
The agreement was that they would swap after a year.
Deputy Canney went first, then stepped down - with Deputy Moran then becoming minister.
Last week it was decided that, instead of switching again, Deputy Moran would stay in the role.
Sean Canney is considering leaving the Independent Alliance over the perceived snub.
Sinn Féin leader Mary Lou McDonald has suggested it's an inappropriate row.
She argued: "This is the business of Government, and ministerial positions being handed out like baubles, or rewards... almost like guys arm wrestling over who would be a minister or not.
"It just seems to me to be terribly inappropriate."
The Independent Alliance met Deputy Canney yesterday, and asked him to explain his future by tomorrow.
The Galway East TD has also met with the Taoiseach, and is now understood to be consulting with his support base.
Deputy Canney is the Government deputy chief whip, which comes with a €15,000 top up salary.
It is unclear if he could keep that role outside the Independent Alliance.