The fine for failing to shovel sidewalks in Boston could skyrocket to $1,500 for some property owners under a bill the Legislature sent to Gov. Charlie Baker yesterday — just in time for winter.

Pushed by Mayor Martin J. Walsh after 2015’s record-setting winter — when some property owners took fines rather than deal with the mountains of snow — the bill would raise the cap on fines from $300 to $1,500 for homeowners and businesses that don’t shovel their sidewalks, or who heave it onto city streets.

“I’ve worked in and around government for 12 years, and I’ve never seen such widespread snow issues that we saw two years ago,” said state Rep. Dan Hunt, a Dorchester Democrat who filed the bill. “One snow contractor would push the snow across the street or on someone else’s property. Or construction people would dump the snow on the sidewalk, and those guys wouldn’t be able to remove it because it would be 10 or 15 feet high.

“Obviously there were extreme circumstances, but you don’t want to have the conversation about how do we stop that two years from now when there’s a crazy amount of snow.”

The Senate and House both passed the legislation yesterday, sending it to Baker’s desk for his signature. A Baker spokeswoman said he is reviewing it.

A schedule for fines is still being worked out. The city intends to impose a higher cap for commercial businesses and buildings with six or more residential units. For buildings with fewer than six units, the old cap of $300 will stay, according to Walsh’s office, which added it could take several violations for a scofflaw to hit the cap.

In a statement, Walsh said, “It’s vital all businesses and residents do their part to make sure our cities and towns across the Commonwealth are safe,” he said.

Neighborhood associations cautiously applauded the move.

“As an involved downtown resident, I do think fines are appropriate. … But there are residents who aren’t going to pay attention. A $300 fine is nothing for them,” said Sarah Herlihy of the Bay Village Neighborhood Association. “But there should be a sliding scale and some structure around it so discretion is used appropriately.”

Jim Coveno of the City Point Neighborhood Association in South Boston said he thinks the “majority (of residents) would be encouraged” by the change. “Most of them do a pretty good job of shoveling in Southie anyway,” he said. “Typical Southie attitude, the sort of shame-your-neighbor-into-doing-what’s-right (approach).”