"This is a dangerous and very challenging weather event," Nutter said.
Widespread flooding and record-breaking tidal surges are likely, he said.
Extra police and fire personnel will be on duty through the storm, the mayor said, and he said roads should be clear for them.
"If you don't need to be out tomorrow, please stay home," said Nutter.
City Council President Darrell Clarke took it one step further.
"Hopefully, the utilities will stay on," Clarke said. "Even if they don't, stay home."
Nutter told city employees, with the exception of emergency personnel, to stay home on Monday.
Trash will not be picked up on Monday; those city residents with Monday pickup days are asked to keep their trash for an extra week.
By early evening, the city's emergency management center – a command room in the Fire Department's administration building - had been activated. It will be fully operational by 6 a.m., Nutter said.
The mayor said he had spoken to President Obama, who offered help if the storm is as bad as promised.
"The president emphasized that FEMA is ready for action to deal with Hurricane Sandy," Nutter said.
Contact Kristen Graham at 215-854-5146, firstname.lastname@example.org or on Twitter @newskag.