Four explosions hit three different neighbourhoods in the Morocco-controlled city of Smara, damaging two houses, local authorities told AFP.
The attorney general "has entrusted the investigation team with carrying out the necessary technical and ballistic expertise to identify the origin and nature of the projectiles," said a statement quoted by Morocco's MAP news agency.
Two people who suffered serious injuries were transferred to a hospital in Laayoune, 200 kilometres (around 125 miles) west of Smara, while a third who suffered minor injuries went home after receiving medical treatment.
Images on social media which AFP could not verify, show the partially collapsed roof of an empty house as well as some metal debris.
Western Sahara has been embroiled in a conflict that dates back to 1975 when former colonial power Spain withdrew, sparking a 15-year war between the Algeria-backed Polisario Front and Morocco for control over the territory.
That ended in a 1991 ceasefire deal with the North African kingdom in control of 80 percent of the resource-rich desert region and the Polisario clinging to hopes of a UN-supervised referendum on independence provided for in the deal that has never taken place.
It is considered by the United Nations to be a "non-self-governing territory."
On Thursday, the Polisario Front said in a statement that it had "targeted strongholds of Moroccan occupation forces near Hanka Houria" in the Smara region.
"The attacks by the Sahrawi army continue against the Moroccan occupation forces, which are suffering heavy human and material losses along the wall of shame," it added.
The wall, which was erected by Morocco in the 1980s, stretches over 2,700 km (around 1,677 miles) and separates the Morocco-controlled part of Western Sahara from the territory the Polisario considers "liberated."
In late 2020, the Polisario declared it was "in a state of legitimate defence war." saying it viewed the entire Western Sahara area as a war zone.
In response, Morocco's king said he remained committed to the ceasefire, expressing a "firm determination to respond, with the greatest severity, and within the framework of legitimate defence, to any threat."
The UN Security Council in October 2022 called for Morocco, the Polisario, Algeria and Mauritania to resume negotiations that have stalled since 2019.