Both yes and no. Since the e-cigarette is not a cigarette it’s not covered by the Swedish smoking ban. However, it is up to employers and owners of shops and restaurants whether they choose to allow e-cigarettes or not in their premises. All trains and airplanes in Sweden have a ban on e-cigarettes.
If you encounter a shop or restaurant that does not allow e-cigarettes, feel free to explain to them what an e-cigarette is and why it should be allowed. The same goes when meeting people with dubious views about e-cigarettes, then it is appropriate to objectively explain the opposite.