The message, written Hindi and being circulated since yesterday, claimed that the clash occurred between two communities at Pathanwadi area in Malad on Sunday.
Terming the message as "totally misleading", police spokesperson and DCP Ashok Dhude said no such incident took place in the said area.
A case has been registered against five persons at Kurar police station for spreading communal hatred and for rumour mongering on social media, he said.
Police have withheld the names of the accused.
They have been booked under section 153 (a) (promoting enmity between different groups), 295 (a) (deliberate and malicious acts, intended to outrage religious feelings), and 120 (b) (punishment for criminal conspiracy) of IPC, Dudhe said.
Meanwhile, police have appealed to the citizens not to believe in such rumours.