No. An opportunity attack grants you a single melee attack. Shoving requires taking the Attack action.

See PHB pg 195.

Opportunity attack:

You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature.

Shoving:

Using the Attack action, you can make a special melee attack to shove a creature prone. If you're able to make multiple melee attacks with the Attack action, this attack replaces one of them.

For much the same reason, an opportunity attack also only grants you a single melee attack and not the multiple attacks granted by the Attack action.

Jeremy Crawford states that one way to shove outside of your turn is to take the ready action to prepare a grapple/shove when your target escapes your reach.

Grappling/shoving are part of the Attack action (PH, 195). Take the Ready action to grapple/shove outside your turn. [Sage Advice]

Note that this means you sacrifice your Action on your turn.

Also see related for grappling: Can you make a grapple attack as an Attack of Opportunity

No. An opportunity attack grants you a single melee attack. Shoving requires taking the Attack action.

See PHB pg 195.

Opportunity attack:

You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature.

Shoving:

Using the Attack action, you can make a special melee attack to shove a creature prone. If you're able to make multiple melee attacks with the Attack action, this attack replaces one of them.

For much the same reason, an opportunity attack also only grants you a single melee attack and not the multiple attacks granted by the Attack action.

Jeremy Crawford states that one way to shove outside of your turn is to take the ready action to prepare a grapple/shove when your target escapes your reach.

Grappling/shoving are part of the Attack action (PH, 195). Take the Ready action to grapple/shove outside your turn. [Sage Advice]

Note that this means you sacrifice your Action on your turn.

Also see related for grappling: Can you make a grapple attack as an Attack of Opportunity

No. An opportunity attack grants you a single melee attack. Shoving requires taking the Attack action.

See PHB pg 195.

Opportunity attack:

You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature.

Shoving:

Using the Attack action, you can make a special melee attack to shove a creature prone. If you're able to make multiple melee attacks with the Attack action, this attack replaces one of them.

For much the same reason, an opportunity attack also only grants you a single melee attack and not the multiple attacks granted by the Attack action. See related: Can you make a grapple attack as an Attack of Opportunity

No. An opportunity attack grants you a single melee attack. Shoving requires taking the Attack action.

See PHB pg 195.

Opportunity attack:

You can make an opportunity attack when a hostile creature that you can see moves out of your reach. To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature.

Shoving:

Using the Attack action, you can make a special melee attack to shove a creature prone. If you're able to make multiple melee attacks with the Attack action, this attack replaces one of them.

For much the same reason, an opportunity attack also only grants you a single melee attack and not the multiple attacks granted by the Attack action.

Jeremy Crawford states that one way to shove outside of your turn is to take the ready action to prepare a grapple/shove when your target escapes your reach.

Grappling/shoving are part of the Attack action (PH, 195). Take the Ready action to grapple/shove outside your turn. [Sage Advice]

Note that this means you sacrifice your Action on your turn.

Also see related for grappling: Can you make a grapple attack as an Attack of Opportunity