He is said to have been killed in front of a large crowd of government officials as a way of setting an example to Kim's other subordinates.
The dictator's uncle, Jang Song Thaek, was killed in 2013 after being described as "despicable human scum" by state media and charged with treason and corruption.
Unlike other purges, which happen in secret, Jang's death was publicly trumpeted by the North Korean regime, which accused him of having "perpetrated thrice-cursed acts of treachery".
Dozens of other officials are believed to have been killed since Kim took power following the death of his father, Kim Jong Il in 2011.
Choe is reported to have taken office in June last year.
He once led the North Korean delegation in economic co-operation talks with South Korea. He was also a former member of the Supreme People's Assembly, the North Korean parliament.
South Korea's ministry of unification, which is responsible for relations with its neighbour, said it was "closely monitoring the possibility of any changes in Choe's circumstances".
Reports of executions in North Korea are sometimes attributed to South Korean intelligence officials but often rely on anonymous sources.
South Korea's Yonhap news agency said someone "with knowledge of the North" had reported Choe's execution.
The North Korean government is a labyrinth of overlapping committees and Choe is believed to have been one of at least seven vice-premiers.