Fr Tom Uzhunnalil, an Indian Salesian priest, was praying in the chapel of a care home run by nuns in the capital Aden when the militants murdered 16 of them earlier this month.
The gunmen then kidnapped Fr Uzhunnalil.
Indian authorities confirmed soon after the incident that he was kidnapped, and that attempts to rescue him had begun.
Yemen is a conflict zone.We do not have Embassy there.But we will spare no efforts to rescue Father Tom Uzhunnalil. https://t.co/9fsteD712b
— Sushma Swaraj (@SushmaSwaraj) March 6, 2016
No one has claimed responsibility for the murder of the 16 nuns at the care home or the priest's kidnap, however a Catholic sorority based in South Africa has said Islamic State was behind the massacre.
The Franciscan Sisters of Siessan said in a post on Facebook: "Was informed that the Salesian priest, Fr.Tom who was kidnapped by ISIS from the Missionaries of Charity Home in Yemen is being tortured and is going to be crucified on Good Friday.
"This calls for serious concerted prayers from all of us."
The post has since been removed, after Fr Tom Uzhunnalil's own order - the Salesian's Bangalore - said they could not verify that information.
Father Mathew Valarkot, a spokesman for the order, said: "We have absolutely no information on Fr Tom.
"But even today we do not know who has taken him and what their motives are because no one has claimed responsibility."
