First: There isn't an equivalent.
Wizards cannot, by Rules-as-Written, get Metamagic. They just don't have access.
But, don't worry, there's a few things you might be able to do.
1. Three Sorcerer levels
Taking Three levels in Sorcerer (provided your DM allows you to Multiclass) grants you access to the Subtle Spell metamagic. You'll have three points to spend (so three times per day) and can be subtle with spells.
When you cast a spell, you can spend 1 sorcery point to cast it without any somatic or verbal components
2. Just play a Sorcerer
Sorcerers and Wizards aren't ALL that different at a mechanical level. Depending on exactly what you're trying to achieve with the character, there's little reason (if any) that you couldn't just play a sorcerer that is old, robed, has a righteous beard, and likes to hang out with halflings.
3. Work with your DM to make a custom feat
A little feat goes a long way. Talk with your DM about a homebrew option that gives you a more limited version of metamagic and/or metamagic points. My first thought is something along the following lines:
You gain access to one metamagic ability costing one point, as per the sorcerer's available options, as well as two metamagic points that recharge after a long rest.
Maybe it should be three points, or maybe you should be able to convert slots into points, OR maybe even you just get to use subtle spell twice per long rest. That's a conversation between you and your DM.
4. Custom Spell (credit Kamil Drakari)
Work with the DM to create "new spells" that are existing spells but without verbal/somatic components (probably at higher level than the original version). That would keeps Sorcerers as "flexible casters who can modify spells on-the-fly" while a wizard can get the same effect but needs to prepare for it ahead of time.