Patsy Kelly, a member of Derry City and Strabane District council, is alleged to have offered his support to Sinn FÃ©in's Pat Doherty on social media during the Westminster elections.
In a statement, the SDLP said an investigation had been launched into the matter.
The whip will be withdrawn from Mr Kelly for a period of four weeks.
The SDLP has withdrawn the whip from a councillor for an alleged breach of discipline on social media.