Checks within the Department of Health have not revealed a problem with supply of the medicine, said Steve Barclay.
The National Pharmacy Association earlier said there were “blips” in supplies of liquid penicillin, which is often given to children.
The level of supply is “not a concern at the moment”, said Mr Barclay but stock could be moved around if there was an issue with particular GPs getting supplies.
The Association of Independent Multiple Pharmacies, which represents about 4,000 chemist businesses, said many were struggling to obtain all they need.
“We’re in very close contact with our medical suppliers," Mr Barclay told GB News. "They’re under a duty to notify us if there are supply shortages. They have not done so as yet.
“I checked with the team last night — we have an established team in the department that does this on a permanent basis — and they reassured me we have good supply," he told Sky News.
“The medical suppliers are required to notify us if they’ve got shortages.
"Now, sometimes GPs can have particular surges if they’ve got a lot of demand in an area and that’s quite routine … we can move the stock around our depots.
“As of last night when we checked [with suppliers], they said they could reassure us that they’ve got good stock and were moving that around to meet demand.
“Obviously parents are concerned at the moment because they see the stories. One in five children have this — Strep A — naturally and complications are very rare, but it’s important that we’re vigilant.”
Dr Leyla Hannbeck, chief executive of the Association of Independent Multiple Pharmacies, told PA: “Mr Barclay is saying there’s no shortage of antibiotics, yet when people go to their pharmacy they are finding there is no stock.
“Pharmacies across the country are reporting that they are struggling to get stock from wholesalers.”
To date, at least nine children across the UK have died from complications caused by the Strep A infection.
The most recent death reported was of Stella-Lilly McCorkindale, who attended Black Mountain Primary School in Belfast, Northern Ireland.
The school has spoken of its “tragic loss” and said, “the thoughts of the entire school are with the pupil’s family and friends at this difficult time”.
In Scotland, health officials reported that there have been 13 cases of invasive Strep A in children aged under 10 since the start of October.
UK Health Security Agency officials have suggested that a lack of mixing because of the Covid pandemic and susceptibility in children are probably “bringing forward the normal scarlet fever season” from spring to this side of Christmas.
Dr Colin Brown, deputy director of the agency, suggested on Tuesday that the strains are not more severe.
“There isn’t something that is particularly new or novel about the bacteria that are causing the infections that we’re seeing at the moment,” Dr Brown said.
Later on Wednesday, Prime Minister Rishi Sunak said parents should seek help if they thought their child was affected.
“We are seeing a higher number of cases from Strep A this year compared to usual," Mr Sunak said.
“What I can say is that the NHS … is working very hard to make sure parents are aware of the symptoms that they should be looking out [for] because this can be treated appropriately with antibiotics.
“There are no current shortages of drugs available to treat this and there are well-established procedures in place to ensure that remains the case.
“There is no reason to believe that it has become more lethal and more resistant to antibiotics, so the most important thing for parents to do is look out for the symptoms and get the treatment that is available for them.”
The agency has advised medics to have little aversion to prescribing antibiotics for children who may be suffering infection linked to Strep A.
On Friday, it said GPs should also “maintain a low threshold for prompt referral” to hospital of any children presenting with persistent or worsening symptoms.
Strep A bacteria can cause many different infections, ranging from minor illnesses to serious and deadly diseases.
They include the skin infection impetigo, scarlet fever and strep throat.
While the vast majority of infections are relatively mild, sometimes the bacteria cause serious and life-threatening invasive Group A Streptococcal disease.
This occurs when the bacteria have invaded parts of the body such as the blood, deep muscle or lungs.
Two of the most severe, but rare, forms of invasive disease are necrotising fasciitis and streptococcal toxic shock syndrome.