Prepare the potatoes according to package directions: Remove and discard the cardboard and plastic film. Mix the potatoes with the olive oil and enclosed seasoning package. Cook until the potatoes are tender, 30 to 40 minutes.
Let the potatoes rest until cool enough to handle.
Place the tomatoes and mozzarella balls in a medium bowl. Toss with the olive oil and salt.
On to each skewer, thread 1 tomato, 1 mozzarella ball, 1 basil leaf and 1 potato.