The Manchester United forward was pictured performing a crude gesture after one of his side's goals during their 3-1 win over Saints.
United came back from a goal down to win 3-1 at Old Trafford thanks to Amad Diallo's hat-trick.
The Ivorian scored three times in 12 minutes, including in the 90th and fourth minute of stoppage time, to secure all three points.
His heroics sparked passionate scenes amongst his teammates as they celebrated in front of the home crowd.
However, Zirkzee's emotions may have got the best of him as he celebrated one of Diallo's strikes.
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Facing the stands, the Dutch international grabbed his crotch with his right hand.
Similar gestures have previously landed players in hot water with governing bodies.
At last summer's Euro 2024, Jude Bellingham was fined £25,000 and handed a suspended one-match ban for grabbing his crotch during England's win over Slovakia.
Meanwhile, Cristiano Ronaldo was slapped with a one-game ban for gesturing towards fans whilst playing for Al Nassr in 2024.
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The same issue also saw the five-time Ballon d'Or winner fined €20,000 for imitating Diego Simeone's 'cojones' celebration in 2019.
Simeone also received the same punishment as Ronaldo for his antics.
Zirkzee had been a second half substitute for Ruben Amorim's side on Thursday night.
The 23-year-old replaced Rasmus Hojlund in attack as part of a double change in the 53rd minute.
Amorim also threw on Toby Collyer in place of Manuel Ugarte as part of the alteration.
Instead of his substitutes, though, it was Diallo who rescued the home side against the Premier League's bottom club.
In doing so, he became the second youngest Premier League hat-trick scorer in United's history behind Wayne Rooney.
Speaking at full-time, Diallo told TNT Sports: "In football, you have to believe and we believed until the end.
"We are very happy to win this game. The confidence was there after the draw at Liverpool and win at Arsenal."
He continued: "Yeah, maybe one of the best weeks of my life. I'm very happy for this win as we deserve to win this game.
"We know we have quality players in this time. We need to sometimes have more hunger in the final third. I'm so happy for this win as the team deserve it.
"I'm ready to play every positon, to play wing-back, No.10, wherever the manager wants to put me. I am ready to fight for this club.
"I'm so happy to score a hat-trick."
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