Can I disable unit upgrade from a ruin?

You can edit the game files to remove this specific Ancient Ruins reward.

The data for the rewards is in a file called CIV5GoodyHuts.xml in:

C:\Program Files (x86)\Steam\SteamApps\common\Sid Meier's Civilization V\Assets\Gameplay\XML\GameInfo

Before making any edits, I suggest you make a backup. Then open the file in notepad/other text editor and remove the following values:

<Column name="UpgradeUnit" type="boolean" default="false"/>

and:

<Row>
        <Type>GOODY_UPGRADE_UNIT</Type>
        <Description>TXT_KEY_GOODY_UPGRADE_UNIT</Description>
        <Sound/>
        <UpgradeUnit>true</UpgradeUnit>
    </Row>

shanondin's answer was helpful but didn't fully solve the problem. Starting from their solution I was able to find other places where the upgrade was referenced.

Rather than delete the reference in the XML file I opted to learn the mod tools and alter the game that way.

The mod I created is available in the steam workshop here. The zip file for the mod is attached to this forum post.