Berahino, who has scored eight goals in all competitions for West Brom this season, was stopped by police last month.
He was arrested on suspicion of drink-driving before being released on bail, with the news breaking this week.
In a media conference on Thursday, Irvine conceded that he was surprised to learn about the incident.
"I found out on Monday while I was at the Aston Villa [versus Southampton] game," he said.
"The phone call was a shock, but then of course we don't know all the circumstances and the details of the investigation. Until then I can't actually make any kind of decision one way or another.
"I haven't spoken to him about the investigation because I don't think that's anything to do with me.
"I have spoken to him about the football side. He's trained really well this morning. The club are looking at everything that's going on."
Berahino is in line to face Arsenal in the Premier League on Saturday, despite suffering a tight hamstring earlier in the week.
"Saido didn't train on Tuesday," Irvine added. "He trained on Thursday and trained really well. I'm certainly perfectly happy with the way he went about things.
"I'm not necessarily feeling that he should have come to me. I don't really know exactly what the circumstances are and until the investigation is concluded I probably won't. I've just got to deal with the football side."
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