Hurley has always maintained Bing is the father
The Hollywood producer has issued proceedings in the Family Division, his spokeswoman confirmed on Friday night.
Ms Hurley said she was "extremely distressed" and said she found the High Court action "astonishing".
Mr Bing's spokeswoman said that if it is proved he is the father of Ms Hurley's son Damian, he will want to support him and be involved in his upbringing.
Bing has instructed a firm of UK solicitors to handle the case.
The action comes after Hurley gave birth to Damian on 4 April.
The single actress and model has always maintained that Bing is the father.
Court date
The court could order DNA tests to be carried out on Damian if the two parties fail to reach an amicable agreement.
The spokeswoman said: "Now that Ms Hurley has had her baby, Mr Bing is anxious to establish beyond any doubt who is the baby's father.
"If it is proved that Bing is Damian's father, he would wish generously to support him and to be involved in his upbringing."
She said that because her client had been unable to contact Hurley, or any of her solicitors to discuss the issues privately, he has been obliged to instruct his UK solicitors to issue proceedings in the Family Division in the hope of "bringing these matters to a quick and amicable resolution".
Bing has previously questioned the paternity, saying their relationship had not been "exclusive".
Hurley countered these allegations, saying she had been "completely loyal and faithful" during their 18-month relationship.
She claimed on Friday that he had made no effort to get in touch with her following Damian's birth.
A statement on the actress' behalf said: "He has neither called her, written to her or had any mutual friends pass on any messages.
"Elizabeth has always made it clear that she is willing to participate in paternity tests and is extremely distressed that Stephen is attempting to resolve these personal issues publicly."
The 36-year-old and her son have not been seen out in public since the birth.
They have been staying at Sir Elton John's secluded mansion in Windsor, Berkshire.
She is believed to have negotiated a £1.5m deal for exclusive pictures and the story of the birth with a glossy magazine.