The Daily Telegraph and Daily Express made the claims after Defence Minister Penny Mordaunt announced in Parliament she'd written to the churches who provide chaplains to the chapels asking them how they intend to follow the law, which allows gay weddings.
Currently churches are exempt from same sex marriage legislation but chapels are not considered to be in the same bracket.
In 2014 parliament passed rules meaning gay weddings could take place in the 190 military chapels in England and Wales, despite fierce opposition from Tory MPs.
No gay marriages have happened in military chapels since then because chaplains from churches have refused to be involved.
But now Ms Mordaunt has written to those concerned re-emphasising the law and saying she has to "consider the rights" of gay military workers.
The new rules allow for chaplains to express their opposition to gay marriages but do not allow them to be exempt from conducting the services if asked to by officials.
Responding to a question in parliament Ms Mordaunt said: "There are 190 military chapels in England and Wales registered for marriages under the rites of Church of England or otherwise, as described under sections 69 and 70 of the 1949 Marriage Act.
"The Ministry of Defence allows same-sex marriages in military chapels, but none of the Sending Churches using the chapels currently allows same-sex marriages to be conducted there.
"I have asked the Chaplaincies of the three Services to advise me on how Parliament's sanction of same sex-marriages may be fully implemented."
The Ministry of Defence has said in a statement: "An article in The Daily Telegraph claims incorrectly that church leaders have been ordered to allow same-sex marriages in military chapels.
"The paper says that Defence Minister Penny Mordaunt has written to military chaplains after churches using the chapels refused to allow the ceremonies. According to the article, the move comes 18 months after regulations were passed to allow same-sex marriages in the 190 military chapels in England and Wales.
"The MOD supports same-sex marriage and is committed to ensuring that couples are not disadvantaged by their service. However, as in the civilian world, it is not permitted to perform same-sex marriages in a church."