B737-800
Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine
Inflight Event / Encounter Fuel Issue; Inflight Event / Encounter Weather / Turbulence
Air Traffic Control Issued New Clearance
Procedure
We did a Go Around with a subsequent wind shear encounter due to the fact that you cannot deviate from the arrival and approach once you are below a certain altitude. With better ATC guidance; which we requested; we would have held or divert to the alternate airport. Having done the Go Around we got ATC clearance to fly to ZZZZ. We landed with low fuel indicated in both main tanks. We had 4K lbs on board.  We were a few hours late and did not have correct information to avoid the situation. It would be a good idea to carry more fuel than just what is required to satisfy max landing weight. The excess fuel can be burnt off in the holding pattern before landing.
B737 Captain reported that a go-around and diversion resulted in landing with low fuel.