Henry named Tamou in his starting line-up on Tuesday but confirmed the club would decide if it would discipline Tamou on Wednesday.
The Cowboys have also tendered a report on the incident to the NRL's integrity unit.
Tamou copped a one-week ban from the club in 2011 for breaking team alcohol rules but Henry said on Tuesday: "You have to treat everything on its merits.
"It's a different incident (to 2011) and he hasn't had any problems in between.
"He is very remorseful about it (drink driving) but we will have a discussion about whether it warrants missing out on football."
Police confirmed a 24-year-old Kirwan man was pulled over in the Townsville suburb of North Ward about 3.30am on Monday and charged after allegedly recording an alcohol concentration of 0.197.
Tamou has been charged with unlicensed driving and driving under the influence of alcohol and will appear in Townsville Magistrates Court on July 2.
A club statement said Tamou would not contest the charge.
Asked if Tamou's arrest had added to the pressure on the club, Henry said: "It doesn't help.
"But it's done and how you react and cope with it is important.
"We have to get on with life. It won't be a distraction or an excuse on how we perform on Friday night.
"As a club we have a game of football to win down there.
"We are desperate now for two points. It's a massive game for the club."
In some welcome good news, co-captain Johnathan Thurston returns from a groin injury after failing to back up from Queensland's Origin I loss last weekend.
Henry hoped fatherhood had been kind to Thurston who welcomed the birth of his first child last week.
"(Thurston's fiancee) Sam is due back (from hospital) this week but her family and Johnathan's are up so I am hoping he is handing her (baby) over and getting his rest because we need him to be fired up and ready to go," Henry said.
"I am sure he will.
"It's been a while since we sang our victory song and that can be disheartening but if you watch the boys train and in the gym the camaraderie is there.
"The season is not over and we are a chance but we need to string some wins together - we need to start Friday night."
-AAP