Shoving (PHB p. 195) states:
Using the Attack action, you can make a special melee attack to shove a creature
Can the additional attack action granted by the haste spell also be used to shove a creature?
[...] it gains an additional action on each of its turns. That action can be used only to take the Attack (one weapon attack only) [...] action.
Shoving a creature is a:
[...] special melee attack [...]
but it's not stated to be a weapon attack.
Therefore, you cannot use your hasted action to shove a creature.