The State Security Service of Ukraine (SBU) said a group of criminals had been trying to sell the uranium-238 isotope -- common in nature and often found in phosphate fertilisers -- to an unknown client at the time of their arrest.
The SBU said the incident occurred on Wednesday and was immediately reported to Ukrainian President Petro Poroshenko.
"Four members of a criminal group that was trying to sell the nuclear material were detained with the evidence on hand," Interfax quoted an SBU statement as saying.
"According to preliminary information, the nuclear matter was uranium-238."
The reported incident came with Ukrainian media filled with speculation about pro-Russian rebels' ability to develop a so-called "dirty" nuclear bomb that releases small but lethal doses of radiation over wide areas.
Ukraine gave up its nuclear arsenal with the collapse of the Soviet Union in 1991.
But the east European nation is still filled with nuclear storage facilities and decades-old disposal sites.
Ivano-Frankivsk lies in the heart of Ukraine's nationalist western part of the country and remains untouched by the 16-month separatist war.