Is sweat najis in Islam?

No. Human sweat is pure in Islam. It doesn't make your clothes, prayer mat or gym equipment impure, and it doesn't affect your wudu or prayer. Sweat can smell, so hygiene and courtesy matter, but a smell is not the same as being najis (ritually impure).

What najis actually means

Najis is a short, specific list of substances that must be washed off before prayer, such as urine, feces, vomit and flowing blood. Dirt, grime and bodily moisture in general are not on that list. Scholars have long treated human sweat, saliva and tears as pure. If you're unsure whether something is najis, the starting point is that it's pure until you know otherwise.

What the Prophet ﷺ taught

When Abu Hurairah avoided the Prophet ﷺ because he was in janabah, the Prophet ﷺ said, "Subhan Allah! A believer never becomes impure" (Sahih al-Bukhari 283). The body of a Muslim is not impure just because it is in a ritual state or has been working hard.

Aisha described how the Companions did their own manual labour, so their sweat used to smell, and they were advised to take a bath (Sahih al-Bukhari 2071). Notice that the advice was about cleanliness and courtesy. Nobody told them their clothes were impure or their prayers invalid. See Does sweating at the gym break wudu?

Sweat on clothes, mats and equipment

Clothes: sweaty T-shirts and leggings are pure. You can pray in them if they cover you properly. See Can I pray in sweaty workout clothes?
Prayer mats and yoga mats: pure, even if they're damp with sweat.
Gym benches and machines: pure too, although wiping them down is good manners.
Sweat in janabah or on a period: still pure.

When sweat is mixed with something najis

The sweat itself is pure, but it can carry something najis with it. If you've cut yourself and blood has soaked into your shirt, or urine has leaked onto your shorts, the najis part still needs washing. Most scholars excuse a tiny spot of blood. See Is blood najis?

Smell is a courtesy issue

The Prophet ﷺ cared about clean, pleasant presence in shared spaces. He told people who had eaten raw garlic or onions to keep away from the mosque, because the angels are harmed by what harms people (Sahih Muslim 564). Many scholars extend this to any strong smell, including heavy body odour. So after a workout, it's good manners to:

Shower or wash up before joining a congregation or visiting a mosque.
Change into a fresh shirt.
Use unscented or lightly scented deodorant.

If you only have a few minutes before a prayer time ends, pray in your sweaty clothes rather than miss the time. See Where can I pray at the gym?

Key points

Human sweat is pure, not najis.
Sweaty clothes, mats and equipment don't affect prayer.
Blood or urine mixed with sweat still needs washing.
Smell is about courtesy: wash and change when you can.

Tip: Keep a spare T-shirt and a small deodorant in your gym bag. It takes one minute and means you can pray or go to the mosque straight after training.