Some residents of the capital of North Kivu province said a bomb had landed near a school in the Mugunga district on the city's edge while others said it was a mortar shell.
"We don't know if it came from the enemy or if it was friendly fire," said a security source, speaking on condition of anonymity.
The army spokesman in North Kivu, Guillaume Ndjike, said the M23 had opened fire from a hillock 20 kilometers (10 miles) from Goma which landed in Mugunga.
Medics reported two people injured while a local resident said a house was destroyed.
After years of dormancy, the M23 movement took up arms again in late 2021 and has since seized vast swathes of Nord Kivu.
The territories of Rutshuru and Masisi in the province have borne the brunt of the fighting between M23 and Democratic Republic of Congo armed forces.
After a lull during the December 20 election which returned President Felix Tshisekedi for a second term, fighting has resumed around Goma.