Offensive slurs were repeatedly chanted at Salima Mukansanga by fans from Kiyovu Football Club as she refereed their 0-0 draw against Gasogi United on Friday evening in Nyamata south of Kigali.
On Wednesday, the club vowed to name and shame those responsible.
"The Kiyovu sports community will not tolerate anyone who disrespects anyone, especially in sports," the club said in a statement.
Rwanda's football federation condemned the abuse and announced late on Tuesday it had launched an investigation of its own.
A government spokeswoman, Yolande Makolo, praised the federation for taking action against "unacceptable behaviour".
"We are with you @RhadiaSalma," she posted on Twitter on Wednesday.
Mukansanga was among three women on the list of 36 referees selected by Fifa for the World Cup in Qatar in late 2022.
It was the first time women had been called up for the men's event, though Mukansanga did not end up officiating a match.
The 34-year-old made history last year by becoming the first woman to referee at the Africa Cup of Nations. She also officiated at the 2019 Fifa Women's World Cup in France.