Golovkin, from Kazakhstan but based in the US, knocked the Polish fighter down three times to claim his 21st stoppage, taking his record to 24-0 in the process.
The British-based Proksa came into the fight having never been knocked down in his career, amateur or professional, but was outclassed by the 2004 Olympic silver medallist.
Golovkin had Proksa on the canvas in the first, fourth and fifth rounds. Referee Charlie Fitch stepped in to stop the contest after 1:11 of the fifth round.
"Proksa is a good fighter, he's strong," said Golovkin. "I feel him. This is my first fight in US. It was not an easy fight for me today [Saturday]. I'm ready to fight. I felt in the first round I was better."
Golovkin's next fight could be against Australian Daniel Geale, who defeated Felix Sturm on a split decision on Saturday in Germany to win the WBA super middleweight title. On Thursday the WBA ordered the winner of the two WBA title fights to meet by the end of the year.
Judges Stanley Christodoulou and Dave Parris scored the fight 116-112 in favour of Geale, with Eugene Grant seeing it 116-112 to Sturm.
It was the German's first defeat since 2006. "Felix has been a world champion for a long time. It was a tough fight," said Geale, who took his record to 28-1 with 15 stoppages.