A senior prosecutor who oversaw the case told the publication the execution had been carried out.
Belarus is the only country in Europe that enforces the death penalty.
In May, the Belarusian Supreme Court upheld a death sentence for Asipovich, who murdered two women in 2018.
Interfax reported that Asipovich was under the influence of alcohol when he attacked two women while drinking with them.
“The women, fearing for their lives, locked themselves inside a bathroom, trying to escape, but the man, armed with a hammer and a knife, managed to break in,” Interfax reported.
Both women died at the scene after being stabbed or struck with a hammer dozens of times.
Asipovich has previous convictions of theft, robbery, hooliganism, and inflicting bodily harm.
For years, the EU has urged Belarus to join other countries in declaring a moratorium on capital punishment.
At least four people were executed last year.
In June, Alyaksandr Zhylnikau, who took part in killing three people, was secretly executed, according to the Parliamentary Assembly of the Council of Europe.
According to rights organizations, more than 400 people have been sentenced to death in Belarus since it gained independence following the collapse of the Soviet Union in 1991.