Centre Reece Lyne has also been stood down from Saturday's must-win First Utility Super League Qualifier 8s game against Halifax RLFC.
Smith, who is in his second spell with the Wildcats, was charged this week with ‘failing to provide a sample for analysis and driving without due care and attention’ after an alleged incident in Hull.
The 30-year-old Australian and former Parramatta half-back will appear before East Yorkshire Magistrates Court later this month.
"The club have been made aware of an incident that occurred ...in Hull,” Wakefield said in a statement.
"A full investigation has been launched and the club are co-operating fully with Humberside Police, the RFL and RL Cares in this matter."
Locke, who joined Wakefield in mid-season in controversial circumstances from Salford after a reported fall-out at the Red Devils, and Lyne are both suspected of being involved in the incident.
Coach Brian Smith said of the incident: "There's been a couple of things that have happened that require the club to deal with so those players have not been selected for this game," he said.
"It's been a distraction for the people who are involved in it but not so much for me or the players.”
Asked if the trio had let the team down, Smith replied: "I'm more excited about this game. It's part of why I came here. I was looking forward to trying to be a part of Wakey's resurgence and hopefully we can continue that."