Lance Bombardier Lynette Pearce – who was unaware of her pregnancy – was rushed to the base's infirmary with stomach pains on Tuesday.
She gave birth in the surgical theatre that is more commonly used to treat victims of bullet and bomb attacks.
The baby is understood to have been five weeks premature.
The Ministry of Defence says a specialist baby- care team was sent to provide care on the flight to England.
Friends of the soldier, who is captain of the Fiji football captain, are overjoyed at the news. Many left messages on Facebook congratulating her.
One said: "Everyone is congratulating her and is really happy for Lynette. We are absolutely stunned at her amazing news.
"She can't believe it and neither can we. Her life is going to totally change.
"I can't wait to see her. She is getting a lot of support from all her friends and family in Britain and in her regiment. She loves the Army and was very keen to fight in Afghanistan.
"She is determined and committed. Now I am sure she will put her son first."
The MoD has not confirmed where the new mother and baby are, but it is believed they are in the John Radcliffe Hospital in Oxford.
A specialist paediatric team was scrambled to the conflict zone to deal with the incident last week.
The 28-year-old servicewoman, who serves with the Royal Artillery, is reported to have left her home country last year to fulfil her dream of serving in the British Army.
The keen sportswoman is the daughter of a former policeman in the Fijian town of Nadi.
She had reportedly passed every fitness test while pregnant and completed all of her military training.
This included an eight-mile march carrying a 25lb backpack.
It is the first time a British soldier has given birth while on active service.