Musfiq Huseynov, a reporter with the opposition "Bizim Yol" (Our Path) newspaper, was jailed for six years in 2008 on bribery charges.
The sentence was later reduced to five years. Huseynov's relatives say the journalist is suffering from tuberculosis in jail and his health is getting worse.
"His temperature is 38 Celsius, it is not coming down. Musfiq says he is measuring his temperature 10 times a day," Huseynov's sister, Dilbar Qasimova, told RFE/RL. "His disease has entered the last medicine-resistant phase. We are very concerned that Musfiq may die."
Rafael Mehdiyev from the Justice Ministry told the Turan agency there was no reason for concern about Huseynov's health.
However, Qasimova said this was misinformation.
She said the treatment her brother was receiving in prison was making his condition worse, not better.
Huseynov's arrest in 2007 was aired on television in a clip purportedly showing him accepting a $3,500 bribe from a man identified as a government official.
Local and international rights groups say Huseynov and two other jailed journalists in Azerbaijan were imprisoned for their critical writings.