Preheat the oven to 350 degrees F (175 degrees C).

Mix flour, butter, sugar, jalapeno, lime zest and juice, and salt together in a large bowl.

Roll dough into 1-inch balls and place on ungreased cookie sheets; flatten slightly with a thumb print to accommodate icing.

Bake in the preheated oven until golden and set, 8 to 10 minutes. Remove cookies from the oven and let cool at least 10 minutes.

Combine confectioners' sugar, lime juice, jalapeno, and lime zest in a bowl. Drizzle icing onto cooled cookies.