Corrections spokeswoman Karen Pojmann said 59 demonstrators gathered on the edge of the prison grounds.
It was the first execution in Missouri since May 2020 and just the seventh in the US this year.
The state moved ahead with executing Johnson despite claims by his attorney that doing so would violate the 8th Amendment to the US Constitution, which prohibits executing intellectually disabled people.
Johnson had a history of scoring extremely low on IQ tests, dating back to childhood. His attorney, Jeremy Weis, said Johnson also was born with fetal alcohol syndrome and lost about one-fifth of his brain tissue when a benign tumour was removed in 2008.
A representative for Pope Francis was among those who urged Republican Govnor Mike Parson to grant clemency, telling Parson in a letter that the pope "wishes to place before you the simple fact of Mr Johnson's humanity and the sacredness of all human life." Parson announced Monday that he would not intervene.
It wasn't the first time a pope has sought to intervene in a Missouri execution. In 1999, during his visit to St Louis, Pope John Paul II persuaded Democratic Governor Mel Carnahan to grant clemency to Darrell Mease, weeks before Mease was to be put to death for a triple killing. Carnahan, who died in 2000, was a Baptist, as is Parson.
In 2018, Pope Francis changed church teaching to say capital punishment can never be sanctioned because it constitutes an "attack" on human dignity. Catholic leaders have been outspoken opponents of the death penalty in many states.
Racial justice activists and two Missouri members of congress — Democratic US Representatives Cori Bush of St Louis and Emmanuel Cleaver of Kansas City —also called on Parson to show mercy to Johnson, who is black.
But Parson announced on Monday he would not grant clemency, and the courts declined to intervene.
Johnson's crime shook the central Missouri city of Columbia nearly 28 years ago.
Johnson was a frequent customer of a Casey's General Store. Court records show that on February 12, 1994, he borrowed a .25-caliber pistol from his girlfriend's 18-year-old son, with plans to rob the store for money to buy drugs.
In a 2004 videotaped interview with a psychologist shown in court, Johnson said he was under the influence of cocaine as he waited for the last customer to leave at closing time. Three workers were in the store: manager Mary Bratcher, 46, and employees Mabel Scruggs, 57, and Fred Jones, 58.
On the video, Johnson said he became angry when Bratcher, who claimed not to have a safe key, tried to flush it down the toilet. He shot the victims with the borrowed gun, then attacked them with a claw hammer. Bratcher also was stabbed in the hand with a screwdriver. Police found two victims in the store's bathroom, and the third in a cooler.
"This was a hideous crime," said Kevin Crane, the Boone County prosecutor at the time. "It was traumatic, and it was intense."
Police officers searching a nearby field found a bloody screwdriver, gloves, jeans and a brown jacket, and questioned Johnson within hours of the killings. At Johnson's girlfriend's house, officers found a bag with $443, coin wrappers, partially burned cheques and tennis shoes matching bloody shoe prints from inside the store.
Johnson had previously asked that his execution be carried out by firing squad. His lawyers argued that Missouri's lethal injection drug, pentobarbital, could trigger seizures due to the loss of the brain tissue when the tumour was removed.
Missouri law does not authorise execution by firing squad.
Johnson was sentenced to death in his first trial and two other times. The second death sentence, in 2003, came after the US Supreme Court ruled that executing the mentally ill was unconstitutionally cruel. The Missouri Supreme Court tossed that second death sentence, and Johnson was sentenced a third time in 2006.
Of the six previous US executions this year, three were in Texas and three involved federal prisoners.
The peak year for modern executions was 1999, when there were 98 across the US. That number has gradually declined and just 17 people were executed last year — 10 involving federal prisoners, three in Texas and one each in Georgia, Tennessee, Alabama and Missouri, according to a database compiled by the Death Penalty Information Centre.