The nature of the information leaked by the soldiers is still being determined.
The soldiers - Lance Naik Ravi Verma from Madhya Pradesh and sepoy Vichitra Behera from Odisha - were taken into custody by Rajasthan police on Tuesday from Jodhpur Railway Station.
Speaking to over phone, Rajasthan's Additional Director-General (Intelligence) Umesh Mishra said Behera has been arrested, while Verma is "cooperating" with the police in investigations.
A local court in Jaipur, where Behera was produced on Thursday, sent him to five days of police custody, he said.
"The soldiers were passing information to Pakistan intelligence through social media as per preliminary investigations. Detailed investigations are underway in the case. Army authorities have been informed about the matter," Mishra said.
"The Facebook user, with whom both the soldiers were in touch, went by the name 'Seerat'. It is not yet clear, however, if the user was a man or a woman. The kind of information they have leaked to the Facebook user is being verified," army sources said in Delhi.
"We are also trying to get custody of the two soldiers from Rajasthan police. Investigations are underway into the matter and disciplinary action will be taken against them," added the Army officer.
An FIR has been registered in the matter by Rajasthan Police in the police station of State Special Branch (Intelligence) in Jaipur under Section 3 of the Official Secrets Act, 1923.
As early as January this year, the Army had issued a list of do's and don'ts - in the form of an advisory - pertaining to social media usage for senior officers, junior commissioned officers and soldiers alike. The advisory was in the form of a list carried pointers including refraining from posting photos clicked in uniforms or those of military locations, installments and equipment.
As per the sources, the advisory list also contained don'ts like 'not giving out names, ranks and deployment locations' and 'accepting friend requests from strangers'.
(Ayaskant Das can be contacted at ayaskant.d@.in)
( With inputs from IANS )