Desumo says the trip out of Wales to have the jab will be at no extra charge
Forty seven parents have immunised their children with the single measles jab at a private clinic despite official advice not to.
The parents from Llanelli and Swansea travelled to a clinic in Worcestershire for the jab.
Wales is dealing with its most serious measles outbreak since the MMR vaccine was introduced more than 20 years ago.
The number of cases has risen to 246 and more than 30 people have been treated in hospital.
Mid and west Wales have seen 179 cases, with around 100 of these centred on Llanelli, Burry Port, south Pembrokeshire and Neath Port Talbot.
The clinic, Desumo, had 50 children signed up for the vaccines in Llanelli on Saturday but could not get a licence to run the clinic in time.
The company said it was responding to public demand in offering parents an alternative to the triple MMR vaccine with the single jab, which is advertised on its website for £75.
The illness is associated with a blotchy rash which spreads down from the face
However, the firm needs approval of Health Inspectorate Wales to work in Wales, a process that could take six weeks, and on Thursday discovered that it would not be licensed in time for Saturday's promotion in the Carmarthenshire town.
So parents who wanted the injection travelled to the clinic on Saturday.
In England, the Care Quality Commission and Medicines Health Regulatory Agency have agreed that Desumo can safely administer single vaccines - even though the National Public Health Service (NPHS) says single vaccines have not been properly tested in the UK.
And health chiefs in Wales have said the single vaccine is a "red herring" and are warning parents against using it.
Wales' chief medical officer, Dr Tony Jewell said he was very concerned about the safety and effectiveness of those vaccines.
He said: "There is no need for parents to spend money on a vaccine when there is a proven, safe and effective alternative in the combined measles, mumps and rubella (MMR) vaccine that has been used across the world for more than 20 years.
"I would urge parents to contact their GPs surgery to arrange for their child or children to receive the MMR vaccine if they have not already had it. It is simple, quick and free."
Many people who catch measles will have a fever, cough, red eyes, and blocked nose and feel generally unwell. The blotchy rash appears a few days later beginning on the face and spreading downwards to the rest of the body over several days.
Typically, people will be infectious from the day before their first symptoms until four to five days after the appearance of the rash.
The NPHS said anyone whose child had symptoms should contact their GP and keep them away from school or nursery for five days after the rash starts.