The storm was expected to dump as much as 18 inches of snow on parts of Cape Cod, where a blizzard warning was in effect. Winds could reach 50 miles per hour, according to CNN meteorologist Dave Hennen.
A blizzard warning was also issued for the South Shore, which stretches from south of Boston to Cape Cod.
On the island of Nantucket, the storm caused some flooding.
Schools and some businesses in Provincetown, Massachusetts, which is on Cape Cod, were closed Monday, and the city ordered motorists to move their cars off the street to make room for snow plows.
In Boston, where a winter storm warning was in effect, forecasters said as much as 7 inches could fall Monday, with more expected Tuesday.
Massachusetts Gov. Charlie Baker said conditions didn't warrant a travel ban, but said residents should stay off roads nevertheless. He ordered state offices to close in the areas forecast to be hardest hit.
"This storm will create hazardous driving conditions for most of today; residents should avoid travel unless necessary," he said on Twitter.
State police reported that roads in parts of Massachusetts were already snow-covered and slick.
Nearly 3,000 Massachusetts Department of Transportation crews were working to help clear roads, the agency said on Twitter.
The speed limit on a stretch of the Massachusetts Turnpike was reduced to 40 miles per hour because of the storm, state police said.
The storm also was starting to snarl air traffic: More than 300 flights were canceled Monday at Boston Logan International Airport, according to FlightAware.com.
Stephanie Coueignoux, a reporter for CNN affiliate WFXT
, said in a tweet that "pellet-like snow" was blowing sideways early Monday in Scituate, Massachusetts.
Meteorologist Eric Fisher with CNN affiliate WBZ tweeted video
of conditions in Plymouth, Massachusetts, showing driving wind pushing snow and waves.
Coastal flooding was also a threat Monday on Martha's Vineyard southeast of Boston and will be on Tuesday in southern New Jersey, Delaware and areas along Delaware Bay, according to the National Weather Service.
The storm was not expected to have a significant impact on Tuesday's presidential primary
in New Hampshire.
The very intense low pressure system producing the storm will remain well south of New Hampshire, and only an inch or two of snow is expected, according to Hennen.
The storm did, however, rough up a Royal Caribbean ship sailing Sunday off Cape Hatteras, North Carolina. "Extreme wind and sea conditions" caused damage to some public areas and guest staterooms aboard the Anthem of the Seas, and four people suffered injuries, none of which were serious, the cruise line said Monday.
The storm forced the ship to head back to New Jersey, its original departure point, the cruise line said on Twitter.
This latest storm comes a little more than two weeks after a massive winter storm
pummeled New York and the Washington region with a few feet of snow.