The directive applies to counties with 20 or more Covid-19 cases, which covers most of Texas’ 254 counties.
Texas hit a record of more than 8,000 virus cases in a day on Wednesday, up from about 2,400 two weeks ago.
Americans are about to mark the Fourth of July weekend, with some beaches coast to coast shut and fireworks displays cancelled.
There have now been 2.7 million recorded infections nationwide and more than 128,000 deaths since the pandemic began.
What did the Texas governor say?
“Wearing a face covering will help us to keep Texas open for business,” Mr Abbott said, announcing the order.
After an initial warning, those who refuse will face a fine up to $250.
“Let me be clear: no-one can ever be put in jail for violating this safe practice,” the governor said.
“Covid-19 is not going away,” Mr Abbott, a Republican, said on Thursday. “In fact it’s getting worse.”
The order includes a series of “common sense” exemptions, including children who are 10 years old or younger, those who have a medical condition that prevents them from wearing a mask, people who are eating or drinking and those who are exercising outdoors.
Texas is now one of 21 states that require mask wearing in public, according to Masks4All, a volunteer advocacy group.
But the move by Mr Abbott was described as “far too little, far too late” by the Texas Democratic Party:
“The move to mandate facemasks comes far too little, far too late for Governor Abbott. It took Texas Democrats demanding that he issue this common-sense policy and record breaking cases and hospitalizations to get Governor Abbott to finally act. This is unacceptable. Governor Abbott continues to lead from behind rather than implementing preventive measures to stop the spread of the coronavirus.
“Texans are still getting sick. Families are still suffering. Texans still don’t know how they are going to put food on the table. All of this could have been prevented if Governor Abbott had listened to experts and medical professionals in the first place.
“Although this is a basic step, there’s still far more work that needs to be done. Governor Abbott and other Texas Republicans must now decide whether they will put more Texans at-risk by holding a statewide convention in the biggest coronavirus hotspot in the country. The decision is theirs.”
How did we get here?
Texas led the charge in US states loosening lockdown measures that were meant to curb the spread of the coronavirus.
Mr Abbott allowed his initial stay-at-home order to expire on 30 April, with almost all businesses operating to at least 50% capacity by early June.
But as the virus surged, Mr Abbott began to walk back his state’s reopening last week, ordering all bars shut and cutting restaurant capacity from 75-50%.
Mr Abbott had initially resisted a state-wide order on masks, going so far as to ban local governments from requiring facial coverings.
What Texans think
Rachel Moon, 23, a sales rep in Houston
When we reopened, my friends all went to the Houston bars, and they have all tested positive now.
I’m a Republican, but I don’t think Trump should be enforcing rules if he isn’t following them.
Genesis Valbuena, 26, project manager, Austin
The reopening should have been done less quickly.
I think initially the decision by local and state government, who closed down everything quickly, was made out of fear instead of data.
What’s the national picture?
Infection rates are rising in 40 of the 50 states, reports the Associated Press, and not all the increases can be explained by expanded testing.
Recent reopenings fuelled job creation at a record pace of 4.8 million in June, according to the US Department of Labour, but employment remains 14.7 million jobs below pre-pandemic levels.
Also on Thursday:
- For the first time, Florida reported over 10,000 new daily cases – more than any European country at the height of their outbreaks, according to Reuters news agency
- Alabama Governor Kay Ivey extended that state’s public health emergency for another 90 days – making it set to expire on 9 September.
- Chicago city officials announced that travellers to the Illinois city from 15 of the worst-hit states will have to quarantine for two weeks upon arrival or face possible fines