ONE B737-NG STRIKES ANOTHER AT AN ADJACENT GATE DURING PUSH BACK.

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WE HAD JUST ARRIVED AT THE ACFT TO START OUR DAY. BOARDING HAD NOT YET BEGUN. THE FO HAD COMPLETED HIS WALKAROUND AND I WAS FINISHING UP MY PREFLT WHEN OUR PLANE SHOOK VIOLENTLY. WE ASSUMED THAT WE HAD BEEN HIT BY A PROVISIONING TRUCK OR SOME OTHER GND EQUIP. I JUMPED OUT OF MY SEAT AND RAN TO LOOK OUT THE JETWAY DOOR. I SAW THAT THE ACFT FROM THE ADJOINING GATE HAD COLLIDED WITH OURS DURING THEIR PUSH. THEIR R WINGLET TRAILING EDGE HAD CRUNCHED INTO OUR L WINGLET LEADING EDGE. I WENT BACK TO THE COCKPIT AND CALLED DISPATCH. MY FO WENT BACK TO THE CABIN TO REASSURE THE FEW THROUGH-PAX WHO WERE ONBOARD DURING THE COLLISION. I WROTE UP THE DAMAGE IN THE LOGBOOK AND SPOKE WITH THE COMPANY MECH AT ZZZ. SUPPLEMENTAL INFO FROM ACN 811346: ON PUSHBACK; WE HAD JUST INITIATED #2 ENG START. THE ACFT TURNED TAIL R WHEN WE WERE PLANNING TAIL L FOR RWY. THEN WE STARTED TO TURN BACK TAIL L WHEN THE ACFT STOPPED SUDDENLY. IT FELT AS IF THE TOW BAR BROKE. THE CAPT CALLED TO THE TUG DRIVER TO SEE IF HE WAS OK. THERE WAS NO ANSWER. HE CALLED ABOUT 3-4 TIMES CONCERNED ABOUT THE DRIVER. HE SAID TO ABORT THE START. I TRIED TO SEE THE TUG DRIVER OUTSIDE AND SAW EXHAUST SMOKE STARTING TO COME FROM THE TUG. WE STARTED TO MOVE FORWARD. I WAS RELIEVED HE MUST NOT HAVE BEEN HURT AND TURNED MY ATTN OUTSIDE. I SAW THAT OUR WINGTIP HAD HIT THE ACFT NEXT TO US. I INFORMED THE CAPT OUR WINGTIP HAD HIT AND WAS DAMAGED. ABOUT THAT TIME THE TUG DRIVER FINALLY ANSWERED HIM AND SAID; 'I'M SORRY; I JUST HIT THE PLANE NEXT TO YOU;' AND PULLED US BACK ON TO THE GATE. THE CAPT MADE AN ANNOUNCEMENT AT THE GATE. THE TUG DRIVER DID NOT SEE THE WING WALKER TRYING TO STOP HIM. THEY NEED TO FOCUS; SLOW DOWN; AND DON'T MOVE THE ACFT WITHOUT BEING ASSURED OF SAFETY AND ALL ACFT CLRNCS. IT SHOULDN'T HAVE HAPPENED. BEAUTIFUL CLEAR DAY; ON TIME.