He was the only survivor of a night-time military operation on Tuesday against a unit of the feared Allied Democratic Forces (ADF) that killed six other fighters, the army said.
A Briton and a South African were murdered along with their guide in an attack on October 17 while on safari in Queen Elizabeth National Park.
Uganda blamed the ADF, an armed militia based in the neighbouring Democratic Republic of Congo that is affiliated with the Islamic State (IS) group.
The IS group later claimed responsibility for the attack, saying it had killed "three Christian tourists."
Uganda's deputy military spokesman Deo Akiiki told AFP that the unit commander, identified only as Njovu, had been injured in the back during a gunbattle on Tuesday.
"This was a successful joint military intelligence-led operation and the whole squad that had been sent by the ADF to cause mayhem, kill tourists, burn schools, hospitals, was eliminated," Akiiki said.
"The only survivor is the commander whom we captured," he said, adding that he was being treated in a secret location and would face trial.
Akiiki said Njovu was found with some of the belongings of the murdered tourists and their Ugandan guide's identity card.
The victims of the October attack have been named as British national David Barlow, his South African wife Celia and the guide, Eric Ayai.
Major General Dick Olum, who oversees Uganda's military operations against the ADF in the DRC, said another six members of the squad were shot dead in Tuesday's operation.
It took place on Lake Edward, which straddles the Uganda-DRC border and lies to the west of the park where the three were slain.
- 'Eliminate splinter groups' -
Olum said the captured fighter had been plotting "another mission to carry out more terror attacks," unaware the military was monitoring the group's movements.
"The squad had seven members including their commander whom we captured. Four of the terrorists were shot and drowned in the water, two tried to swim across the water and were shot dead as well," he said.
"Our mission now is to hunt for the remaining ADF splinter groups and eliminate them."
After the October attack, President Yoweri Museveni called on the security forces to ensure the ADF was "wiped out" and the military has carried out a number of air strikes against its positions in the DRC.
The ADF is historically a Ugandan rebel coalition whose biggest group comprised Muslims opposed to Museveni.
Established in eastern Congo in 1995, the group is accused of slaughtering thousands of civilians in the violence-ravaged region.
In June, ADF fighters killed 42 people including 37 students in an attack on a high school in western Uganda near the DRC border.
Britain has advised its nationals to avoid travel to certain areas of Uganda, including the Queen Elizabeth National Park.
Tourism is a top foreign exchange earner in Uganda, generating almost 10 percent of gross domestic product (GDP) last year, according to government figures.