Young Myla Childs ended up suffering a seizure after having a fever that would not come down on Friday.
It took more than 36 minutes for the ambulance to arrive despite the target from NHS England being that half of Category 1 calls should be attended within seven minutes and 90 per cent in 15 minutes.
Initially the 12-month-old girl was taken to nearby Ludlow GP surgery by her parents, but when the fever continued and no help was available locally they ended up calling 999.
At one point she stopped breathing and her hands, feet and lips went blue before she stopped convulsing, Myla's father Darren said.
He explained: "Friday morning we rang the GP surgery in Ludlow as she had a temperature of 39.9 and it was not coming down no matter how much Calpol or Ibuprofen or whatever we gave her.
"The GP surgery said 'it's just a viral infection, take her home and if she doesn't improve bring her back'.
"About 2pm she started fitting, we rang the ambulance and they were sending one out but because there weren't any available in Shropshire they said it was coming from Hereford."
It would later emerge that Myla had suffered a febrile convulsion, which occurs when a child's temperature rises too rapidly.
He said that no community first responders were on hand - due to volunteers only being trained to deal with cardiac arrest cases - and that the local GP surgery could not send anyone out to help.
Meanwhile West Midlands Ambulance Service (WMAS) had 27 ambulances operating in Shropshire but every one of them was with a patient at the time - whether that be attending a call, travelling to a call or doing a handover at a hospital.
The nearest ambulance was over the county border in Herefordshire.
The 999 call was received by WMAS at 1.47pm on Friday, and according to the ambulance service medics arrived 36 minutes and 59 seconds. However Mr Childs said that by the time the paramedics had donned appropriate PPE, the response time was closer to 50 minutes.
WMAS, which is under more pressure than ever before in its history, has apologised to the family but said using a Herefordshire ambulance was still the right decision.
A spokesman for the service said: “We would like to apologise to Mr and Mrs Childs for the time it took to reach their daughter. Our staff are working tirelessly to respond to patients as soon as we can.
“At the time of the call, all 27 ambulances in Shropshire were with patients, so the nearest available ambulance was sent, from Hereford which is 24 miles away from the location; Shrewsbury is 30 miles away.
“After assessment, the child was taken to hospital as a precaution. They went to Hereford County Hospital as the alternative would have been Princess Royal in Telford which is 31 miles away.”
Mr Childs has now started a petition which is calling for the reinstatement of an ambulance hub in the south of county.
Last year, local ambulance stations closed in Craven Arms, Bridgnorth, Oswestry and Market Drayton. However ambulance bosses said that this would not impact response times due to ambulances always being out on the roads anyway.
Councillors in Shropshire have now called for the return of a Shropshire-only ambulance service in a bid to reduce waiting times but ambulance bosses say further investment is the only solution. Many paramedics are being kept off the road for large parts of their shifts due to the long waits to handover patients to hospitals.
Meanwhile South Shropshire MP Philip Dunne came in for some criticism from Mr Childs for what he described as a lack of support of local first responders and ambulance hubs.
Mr Dunne said: “Mr Childs contacted me on Sunday morning, alerting me to the 50-minute wait his daughter had faced for an ambulance, following her seizure. This must have been traumatic for the family, who have my full sympathy.
"This is the first time he has raised ambulance issues with me. I have been raising ambulance response times with WMAS for months, and have a prearranged meeting with WMAS on Friday, where I shall be raising again the issue of ambulance response times in south Shropshire."