The storm has dumped record rainfall, leaving large parts of the city underwater, homes destroyed and at least 15 people reported dead, the BBC said.
Houston Mayor Sylvester Turner said the curfew was needed to head off looting in America’s fourth biggest city.
The curfew will run from midnight to 5 a.m. for an indefinite period. Relief volunteers, first responders and those going to and from work are exempted.
Turner said the curfew would help prevent “property crimes” against evacuated homes, and was in force “only to prevent potential criminal acts”.
City officials have reported instances of looting, armed robberies and of people impersonating police officers. Thousands have fled their homes in search of emergency shelter amid severe flooding, the BBC report added.
President Donald Trump visited Texas on Tuesday to survey the damage brought by Harvey, calling the storm “epic”. He will not be visiting Houston. The White House said he did not want his visit to disrupt the emergency response.
The rainfall in Texas set a new record for the continental US, the National Weather Service said on Tuesday. Around 52 inches of rain has been recorded since Friday.