Nothing is known about the humor of the ancient Persians.
Here is a sample from Rumi, the 13th century Persian poet who was born in Balkh (Bactra).
A man, hard of hearing, on his way to visit his sick friend, said to himself, "How shall I understand my friend I am going to visit? Well, when I see his lips moving, I will make a guess. When I ask, 'How are you?' he will reply, 'I am fine.' Then I shall say, 'Thanks be to God. What have you had to drink?' He will reply, 'Some sorbet.' Then I will say, 'May you enjoy health. Who is your doctor?' He will say, 'So-and-so.' And I will say, 'I have experienced the benefit of his treatment. Wherever he goes, the desired end is attained.'"