Most vehicles will become hard to control in as little as 6 inches of water and can be swept away in 18 to 24 inches of water.
Maryland Gov. Larry Hogan earlier declared a state of emergency in the flood-stricken area.
The heaviest rain is expected Monday morning.
In Cuba, flooding damaged an oil refinery and caused crude oil to spill into Cienfuegos Bay as the remnants of Alberto continued to drench the island in heavy rain. A number of roads are blocked by flooding, but the exact number was not immediately available.
Information still is preliminary, however, and authorities say they are still checking flooded buildings and streets.
Footage of Sunday's flash flooding showed water surging around cars and pickup trucks and coursing over the top of their wheels. "Also, the road bed may not be intact under flood waters", the agency said in its flash flood watch issue.
Ellicott City, just west of Baltimore, is consistently ranked among the best places to live in America by Money magazine.
A flash flood emergency was issued in Maryland's Howard County at 4:40 p.m.
Some residents of Ellicott City told The Baltimore Sun the flooding appeared to be worse than the 2016 flooding that killed two people and destroyed local businesses. The department also said swift water units from as far away as Northern Virginia were coming to help.