An unpublished decree signed by Kulov on 27 January sacked Bakyt Orunbekov from his post at the Kyrgyz-language "Kyrgyz Tuusu" ("Flag Of Kyrgyzstan").
Orunbekov is a well-known critic of the previous government of former President Askar Akaev.
He was appointed as editor in chief of the government-funded newspaper following Akaev's ousting in March 2005.
Orunbekov says he believes critical articles in "Kyrgyz Tuusu" about Kulov are the reasons for his sacking.
His supporters are planning to rally in the capital, Bishkek,
on 30 January.