Is anxiety a punishment from Allah?

No. Anxiety is not a sign that Allah is punishing you. The Quran says believers will be tested with fear, and the Prophet ﷺ said the people tested most are the prophets and the righteous. Anxiety is a test and a health condition, and Allah wipes away sins through the distress you feel.

Fear is a test, not a verdict

Allah tells us plainly that fear is part of life for believers:

وَلَنَبْلُوَنَّكُم بِشَىْءٍ مِّنَ ٱلْخَوْفِ وَٱلْجُوعِ وَنَقْصٍ مِّنَ ٱلْأَمْوَٰلِ وَٱلْأَنفُسِ وَٱلثَّمَرَٰتِ ۗ وَبَشِّرِ ٱلصَّـٰبِرِينَ "And We will surely test you with something of fear and hunger and a loss of wealth and lives and fruits, but give good tidings to the patient." Quran 2:155

Notice that fear comes first in the list, and the verse ends with good news, not blame. Being tested is a normal part of faith.

The best people were tested the most

Someone asked the Prophet ﷺ which people are tested most severely. He said: "The Prophets, then those nearest to them, then those nearest to them," and that a person is tested according to the strength of their religion (Jami' at-Tirmidhi 2398).

So hardship isn't proof that Allah is angry with you. Often it's the opposite. The Prophet ﷺ himself regularly asked Allah for protection "from worry and grief" (Sahih al-Bukhari 6369). He knew those feelings were real.

Your anxiety is not wasted

The Prophet ﷺ said that no fatigue, disease, sorrow, sadness, hurt or distress befalls a Muslim, "even if it were the prick he receives from a thorn," except that Allah expiates some of his sins for it (Sahih al-Bukhari 5641). Every racing heartbeat and sleepless night counts with Allah.

That doesn't mean you should just suffer through it. Anxiety disorders are common and very treatable with therapy (like CBT) and, when needed, medication. Seeking help is part of trusting Allah.

What can help

Talk to a doctor or therapist if anxiety affects your sleep, work or relationships.
Use the Prophet's ﷺ duas: see What dua can I say when I feel anxious?
Separate guilt from fear: if you made a mistake, repent once and move on. Allah forgives. Endless worry about it is not repentance.
Lean on short phrases when something scary happens. See What do I say when I hear bad news as a Muslim?

When it feels like Allah isn't listening

Anxiety can make you feel abandoned, especially when your duas seem unanswered. That feeling isn't the truth about you or about Allah. See Why isn't Allah answering my dua?

Key points

Anxiety is a test, not a punishment.
Prophets and righteous people were tested the most.
Allah removes sins through your distress.
Treatment and dua work together.

Tip: When anxiety rises, breathe in slowly for four counts, out for six, and quietly say "Hasbunallahu wa ni'mal wakeel" (Allah is enough for us). Repeat until your body settles.