The My Dentist practice in Dolgellau will close on 31 March and the town's other practice is private.
A spokesman for the NHS practice said it had been unable to recruit a permanent dentist in the last two years
The deputy mayor of Dolgellau, Delwyn Evans, told BBC Radio Cymru's Post Cyntaf programme more needed to be done to get dentists into rural areas.
My Dentist clinical director Steve Williams said: "There is a shortage of dentists in parts of rural Wales where long-term unfilled vacancies persist over a significant period of time.
"We have tried unsuccessfully to recruit a dentist for the last two years and, regretfully, can no longer provide services at the Mervinian House Family Dental Practice."
A spokesman for Betsi Cadwaladr Health Board said it intended to re-commission dental services in the area as soon as possible.
"However, there is likely to be a gap between the date of termination of the existing services and the completion of the tender exercise and the re-establishment of new services," he said.
"We are therefore making arrangements for the provision of dental services on a cover basis until a permanent solution can be put in place.
"This will include exploring options for short-term support from the other nearest practices, as well as a dental out-of-hours clinic to operate from Dolgellau Community Hospital for patients requiring urgent unscheduled care."
A Welsh Government spokesman said: "When a dentist decides to reduce or end their NHS commitment, the associated funding remains with the health board to re-commission the service.
"Betsi Cadwaladr UHB has invited applications from dental contractors to help ensure there are NHS services available in the area.
"We expect the health board to continue to review and improve access to NHS primary care dental services through the targets set within its 2016-17 Operational Plan."

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She was beaten by Finland's Enni Rukajarvi, who scored a combined 176.33 from her two best runs out of three.
Ormerod, who won her first World Cup competition last month, scored 146.33 in Innsbruck.
In the men's competition, Rowan Coultas and Billy Morgan finished fifth and sixth respectively.

Criticised by fans last term, Slade entered this campaign under pressure, and the Bluebirds drew their first three games.
But a 2-0 win against Wolves came as a relief to Slade.
"Everybody thought I would be down the road by the end of August, I suspect," he said.
"The pressure was on to deliver at home… and we've managed to do that.
"We're in quite a good place. I see us making progress.
"It was important we got our first win and it will build confidence."
Goals from Kenwyne Jones and Sammy Ameobi helped Cardiff to a comfortable win against a Wolves side who narrowly missed out on the Championship play-offs last season.
Slade succeeded Ole Gunnar Solskjaer as Bluebirds manager in October 2014 and, after a torrid spell around Christmas when Cardiff fans called for Slade's sacking, the former Leyton Orient boss eventually steered his new side to an 11th-placed finish.
Now in his first full campaign in charge, Slade is encouraged with the progress Cardiff are making.
"It is important to get your first win but, performance-wise, I've been fairly satisfied with what we've produced by and large," he added.
"In open play, teams are not causing us problems perhaps like they were last year. We're more organised.
"We're playing off a structure and it's how I want to play now."
Nearly 4,500 patients will lose their only NHS dentist in a Gwynedd town from the end of the month.
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