Hywel Dda University Health Board held a public meeting in Llanelli on Thursday and agreed the reduction should be made with "immediate effect".
It means the paediatric ambulatory care unit (PACU) at Withybush Hospital will be open from 10:00 GMT to 18:00 instead of 10:00 to 22:00.
The health board said it had experienced recruitment problems.
The move means sick children who require assessment after the new closing time will be referred or transferred by ambulance to Glangwili Hospital in Carmarthen.
Speaking on behalf of the health board's Community Health Council, Alyson Thomas said: "It's incredibly disappointing the people of Pembrokeshire are now in this situation.
"We are concerned about the health board's handling of the situation."
The health board's medical director, Dr Philip Kloer, told the meeting there had been "difficulties for some time" with the recruitment of paediatric consultants.
"The action taken to address recruitment during the middle of the year was not as successful as hoped," he said.
The health board's chair Bernadine Rees said the recommendation was accepted with a "heavy heart," but that it was being done on an "interim" basis in the interest of safety.
Plaid Cymru AM Simon Thomas said a "further reduction of services" left him "very concerned at the long term safety at Withybush".
"As a parent I would not have confidence with this service," he said.
"I'm asking for the cabinet secretary for health to take action for the people of Pembrokeshire."
The Welsh Government said the move was so the health board could provide a safe, reliable service.
"What would be unacceptable is for the health board to run a service they know is unsafe," a spokeswoman said.
"It is important to note that the Royal College of Paediatrics and Child Health's review of November 2015 concluded that it would make "no clinical sense" to revert to the previous 24/7 paediatric service model."
Labour AM Eluned Morgan said: "A lack of early action has meant that board members have had no option but to cut PACU by four hours each day.
"I am encouraged that the board has listened to my concerns over taking a more serious and focused approach to managing this service long-term.
"They have provided their assurance that they will work hard to return a 12 hour service for families in Pembrokeshire."
Plans to temporarily reduce the opening hours of a children's care unit in Pembrokeshire have been backed.