Dipash, Akhil and Sreejith were working in a ship, owned by a UAE company, that was seized by the militants in January.
A huge plume of black smoke could be seen rising over the Red Sea city where the Saudi Arabian Grand Prix is taking place this weekend.
The UAE air defence forces and the Coalition Command had succeeded in destroying the missile launcher in Yemen after identifying locations of the sites.
The air defences intercepted and destroyed two ballistic missiles fired by the terrorist Houthi group towards UAE.
The Indian Embassy in UAE said that the mission is in close touch with concerned UAE authorities for further details.
Oil Minister Dharmendra Pradhan said India, the world's third-largest oil consumer, is keeping a close watch on the developing situation.
The Houthis, who control the Yemeni capital, Sanaa, have stepped up their attacks against targets in Saudi Arabia in the past few months.
On June 12, a rebel missile attack on the international airport in the southwestern city of Abha wounded 26 civilians, drawing promises of "stern action" from the coalition.
Three women and two children were among the wounded, who were of Saudi, Yemeni and Indian nationalities.