Joining its predecessors, MLB The Show 16 on PlayStation 3 and 4 will lose its multiplayer and online features as of July 28th. The brief notice has been added to the game’s PlayStation.com page but has not appeared on Sony Europe’s decommissioned servers site.
*Multiplayer and all online features for this product will be decommissioned and will no longer be available on July 28, 2020.
The game remains available to purchase both digitally from the PlayStation Store and of course, on physical media. I’ve added the date to the Watch List calendar. Thanks to @MckissickAllen for pointing out this news.