According to the news agency Reuters, Shishov has now been found dead in a park in Kiev.
His co-worker stated on the messaging app Telegram that he is believed to have gone out to jog in Kiev, Ukraine, on Monday morning, but that he has neither been seen nor heard from since.
He is said to have been reported missing by his partner.
Shishov's friends state that he has recently said that he felt guarded and "persecuted by strangers" during jogging trips, according to the human rights organization Vjasna.
Many Belarusians have fled, often to neighboring Ukraine, Poland and Lithuania, as President Alexander Lukashenko's government has cracked down on all forms of opposition since mass protests erupted after the country's controversial election last year.
Shishov's organization helps newly arrived Belarusians with legal advice and finding housing and jobs in Ukraine, writes the BBC.
On Monday, the Belarusian sprinter Kristina Timanovskaya received protection at the Polish embassy in Tokyo after she refused to return to Belarus from the Olympics in Japan.
On social media, the athlete wrote that she was "kidnapped" by her own leaders to be taken back to Belarus.
Timanovskaya has now been granted a humanitarian visa in Poland, where she is expected to fly on Wednesday.