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."

Ex-Bayern Munich player Dante has helped Nice climb to the summit at the midway point of the season.
They are two points clear of nearest rivals Monaco and five ahead of champions Paris St-Germain.
"Anything can happen. We need to concentrate 100%. We have a chance," said Dante in an interview with BBC World Service's World Football.
Lucien Favre's side have lost just one of their first 19 league games and entertain struggling Metz on Sunday.
"When I wake up I only think to win every game because this season we can make some big dreams come true," added Dante, who joined Nice from Wolfsburg in August.
Former Manchester City striker Mario Balotelli has scored eight goals in nine league games for Nice since joining from Liverpool in August.
Dante said: "Mario is world class. He is so important here and a very good guy.
"Everybody says he is bad boy. Maybe in the last group he made some mistakes but I speak to him and he only wants to play football now."
Listen to World Football's full interview with Dante.

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28 January 2015 Last updated at 07:43 GMT
But apart from sounding impressive - the train in this clip has a really important job.
It's used to clear away old 'ballast', the rocks and stone that support the train tracks, and replace it with new stuff.
It's travelling overnight between Norwich and London at the moment to make sure the train line is in good shape. You can see it in action above.

11 July 2017 Last updated at 15:55 BST
On the tiny island of Muck in Scotland there's only one school with just 9 pupils!
Muck measures just 2.5 miles from east to west and has a population of around 27 people.
Whitney went to spend a day at the island school...
Plans to temporarily reduce the opening hours of a children's care unit in Pembrokeshire have been backed.
[NEXT_CONCEPT]
Nice can "make dreams come true" by winning Ligue 1 for the first time since 1959, defender Dante says.
[NEXT_CONCEPT]
At half a mile long, it's Britain's longest ever train - and can be found travelling through the night with a small army of workers onboard.
[NEXT_CONCEPT]
What's it like to have your whole school in just one class?