Mercado itinerante
 

what do we call in English this kind of markets that go from town to town or from neighborhood to neighborhood once a week?
Itinerant market?

I think a 'traveling market' would be readily understood. 'Itinerant' isn't a well-known word in AmE.

We see peddler shops and (market or street) traders that are only open for a short time or on certain days.

Some other possible options, depending on context, how the market actually works, and what they sell, would be:

Weekly market
Farmer's market (vendors sell food, vegetables, plants, and other misc things)
Saturday market (usually open Saturday & Sunday, vendors sell all kinds of things, with a focus on crafts, handmade things, art, food)

A note on translating things like this. If something doesn't really exist in another culture, you should probably also describe it, in addition to translating it into the other language.