It emerged that Grace was awarded the degree by the university in 2014 after just months of study.
Doctorates typically require several years of full-time research and writing.
“Nyagura has been arrested. We cannot have people who award fake degrees,” Goodson Nguni, a ZACC commissioner told AFP over the telephone.
The professor will be charged with abuse of office, he said, refusing to say whether Grace also faces arrest.
Grace Mugabe’s apparent desire to succeed her 93-year-old husband prompted the army takeover that saw Robert Mugabe ousted from power in November last year.
A copy of the 226-page doctoral thesis, titled “The Changing Social Structure and Functions of the Family” was only published last month following public calls for Grace to be stripped of her PhD.
Critics had argued that Grace, 52, had not actually studied or undertaken research to earn the doctorate.
She was personally capped by then-president Mugabe, who was also the chancellor of the university.