The state, which was among the first to start lifting the lockdown, has seen one of the biggest surges in new US infections, with more than 5,500 new cases on Wednesday.
It is facing a “massive outbreak”, according to governor Greg Abbott, who has urged most residents to stay at home for their safety.
He said: “The last thing we want to do as a state is go backwards and close down businesses.
“This temporary pause will help our state corral the spread until we can safely enter the next phase of opening our state for business.”
The decision does not reverse any of the reopening phases he has already allowed – bars, restaurants, malls, bowling alleys and other businesses can remain open with some capacity limits.
Restaurants can operate at 75% capacity and virtually all other businesses, including bars, can operate at 50%.
Dr Faisal Masud, from the Houston Methodist hospital system, said medics can cope with the rising infections numbers for now.
However, he warned “if this trajectory is what it was the last 10 days when we literally had a tripling of our cases – we can’t do that for a couple weeks at all”.
“This is not good,” he told NBC News. “The explosion of patients all across, that explosion has to slow down.”
Governor Abbott is also stopping elective surgeries to keep beds spare for coronavirus patients in certain counties that are seeing a surge of COVID-19 cases.
Officials from the Centers for Disease Control and Prevention estimate 20 million Americans have been infected with the virus – about 10 times as many as the 2.3 million cases already confirmed.
It means about 6% of the country’s population of 331 million people have contracted COVID-19.
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Earlier this week, the White House’s top expert on infectious diseases, Dr Anthony Fauci, warned the US was experiencing a “disturbing surge” in cases.
More than 36,000 new US infections were recorded on Wednesday, close to the daily all-time high of 36,426 on 24 April.
Texas is among 12 states that have reported record rises in cases this week.
They include Alabama, Arizona, California, Florida, Idaho, Mississippi, Missouri, Nevada, Oklahoma, South Carolina and Wyoming.
Southern and western states like Arizona and Florida that began reopening around Memorial Day, 25 May, are now seeing big spikes in infections.
In California, Disney has delayed the re-opening of Disneyland and Disney California Adventure.
The company had hoped to open its doors on 17 July following four months of closures.
But officials in the state have indicated they will not issue guidelines until after 4 July, sparking the delay.
The firm is also under pressure to delay the 11 July reopening of Walt Disney World in Florida.
The union representing actors at the attraction said the company should postpone welcoming back guests as cases continue to soar in the state.
Meanwhile, California Governor Gavin Newsom has declared a budget emergency, blaming expenses and the economic downturn caused by the COVID-19 pandemic.