The Albion star's wife Jung Hye-Won gave birth last Tuesday morning but, instead of returning to his homeland to see the new addition to his family, the 26-year-old has stayed in England for the start of the new campaign.
Mowbray, himself a father to two young boys, expressed his admiration for the player's commitment to the club.
Mowbray told the Birmingham Mail: "Kim has done exceptionally well. He has got a new addition to the family and he hasn't seen the child yet.
"He is showing a great dedication to his career and loyalty to the team by being here.
"I know if my wife had given birth I would have been asking the manager to leave, even if it was just for a day, to be with my family.
"But he is getting on with his job and is doing really well."
Mowbray added: "We have asked Kim to play in three or four different roles in pre-season and maybe we are still searching for his very best role to benefit the team.
"But he works hard, he is good technically and he will threaten the goal, as we saw on Saturday in the first half an I'm sure he will be fine as we go along.
"He is a good international footballer and we are trying to bring players with that sort of experience to the club if we can.
"Because every day in the Premier League is an event, every day is slightly different and we have to be ready for the big occasion.
"Invariably international footballers have played in big occasions when the expectation is huge and they have to be able to deal with it.
"Kim will have played in many a game when the expectations are high."
