Heorhiy Prakopchyk, an official at labor camp No. 4 in the southwestern town of Ivatsevichy, told Autukhovich's wife, Alena Autukhovich, on December 22 that her husband had cut his wrists but was in "satisfactory" condition.
Prakopchyk did not give the date of the suicide attempt.
Inmates at the labor camp say the incident took place on December 11, after Autukhovich was released from solitary confinement and then told that he would be transferred to another brigade.
Autukhovich reportedly protested that decision and decided to slash his wrists.
The same sources told RFE/RL that Autukhovich has been placed under a "closed regime" (PKT) at the labor camp for a month as punishment for his suicide attempt.
A transfer to PKT means an inmate spends all day and night in a cell either alone or with one or two cellmates. The convict is usually allowed one hour per day to walk outside in a walled square.
It is unclear when Autukhovich began his PKT term.
On December 13, activists of the Vyasna (Spring) human rights center in Minsk said they had information about Autukhovich's transfer to PKT and called the transfer "the continuation of pressure imposed on Autukhovich by authorities."
Autukhovich and three co-defendants were convicted in May 2010 on charges of illegal possession of weapons and ammunition. Autukhovich was sentenced to five years and two months in jail.
The four were originally charged with preparing terrorist acts against officials in their hometowns of Vaukavysk, Hrodna, and Minsk. Those charges were later dropped.
Autukhovich and his colleagues say the cases against them are politically motivated.
He currently has no legal representative and his lawyer, Paval Sapelka, was disbarred in March this year after having represented jailed presidential candidate Andrey Sannikau.
Read more in Belarusian here