Saleh joined the foreign service branch of the 16th Bangladesh Civil Service batch.[3] He had served in the Bangladesh Embassies in South Korea and Australia.[4]
Saleh was the acting high commissioner of Bangladesh in India in 2013.[5] He was the deputy high commissioner of Bangladesh in India in 2014.[6]
In August 2016, Saleh spoke at an event of the Potomac Institute for Policy Studies.[7]
On 30 June 2020, Saleh was made the ambassador of Bangladesh to Belgium.[3] He had been the deputy chief of mission to the Embassy of Bangladesh in the United States.[3] He is also the ambassador of Bangladesh to the European Union.[8] He had worked to move Bangladesh in the GSP Plus scheme of the European Union.[9] In December 2022, he defended the human rights record of the government of Bangladesh at the Briefing on the Human Rights Situation in Bangladesh hosted by Fabio Massimo Castaldo.[10] In April 2023, he met Fu Cong, Head of the Chinese Mission to the European Union and discussed Bangladesh–China relations.[11]