Does burping break wudu?

Why a burp is different from passing wind

Wudu is broken by what leaves the body through the private parts, including passing wind from behind. When a man asked Abu Hurairah what "hadath" (the thing that cancels wudu) meant, he explained it as passing wind, silently or with a sound (Sahih al-Bukhari 135). A burp comes out of the mouth, not from the back passage, so it is a completely different thing. Scholars of the Hanafi, Maliki, Shafi'i and Hanbali schools all list the nullifiers of wudu, and burping, yawning and hiccups are not on any of those lists. See What breaks wudu?

The wudu verse itself describes washing the face, arms and feet and wiping the head, and it doesn't mention air from the stomach at all:

What if a little food or liquid comes up?

Sometimes a burp brings up a small amount of food or acid (reflux). Most scholars (Maliki, Shafi'i, and many Hanbalis) say this still doesn't break wudu. The Hanafi school says vomiting a mouthful breaks wudu, but a small amount that doesn't fill the mouth does not. Either way, just rinse your mouth so you pray with a clean mouth. For more on this, see Does vomiting break wudu?

Burping during prayer

• Your prayer is still valid. A burp you can't hold back doesn't break wudu or the prayer.
• Keep it quiet if you can. Close your mouth and let it pass softly, out of courtesy to the people next to you.
• Don't restart. There's no need to repeat wudu or the prayer because of a burp.

Don't let doubt take over

New Muslims sometimes worry about every small thing that happens in the body during prayer. The Prophet ﷺ taught that a person who feels unsure whether he passed wind should not leave the prayer unless he hears a sound or notices a smell (Sahih al-Bukhari 137). The rule is simple: wudu stays valid until you are sure it was broken. If you notice you are checking yourself over and over, read What is waswas and how do I deal with it?