The answer above doesn't work anymore in Craft 3.7. While duplicated entries are disabled using this hook, saving an existing entry also disables it (even when using ElementHelper::isDraftOrRevision to catch some edge-cases). Probably related to the workflow changes introduced in Craft 3.7. I've opened an issue on Github about this.

Arguably, duplicated entries being disabled or marked as drafts should be the default. I've create a discussion for this feature request. If you care about this feature being implemented, upvote it on Github for visibility.

Using duplicateOf is not sufficient to detect duplicates. A draft, provisional draft or revision being applied to the live entry will also have a duplicateOf property, so this will result in live entries being disabled on save (see this issue on Github for reference).

To be sure the hook only applies to duplicated entries, you also need to check the updatingFromDerivative property – if that is false, the entry is being duplicated.

Here's a complete working hook for Craft 3.7:

use craft\elements\Entry;
use craft\events\ModelEvent;
use craft\helpers\ElementHelper;

Event::on(
    Entry::class,
    Entry::EVENT_BEFORE_SAVE,
    function (ModelEvent $e) {
        $entry = $e->sender;
        if (ElementHelper::isDraftOrRevision($entry)) return;
        if (!$entry->duplicateOf || $entry->updatingFromDerivative) return;
        $entry->enabled = false;
    }
);

In Craft 4, duplicated entries will be disabled by default (see the discussion on Github for reference).