For the measles vaccine to work, the body needs time to produce protective antibodies in response to the vaccine. Detectable antibodies generally appear within just a few days after vaccination. People are usually fully protected after about 2 or 3 weeks. If you’re traveling internationally, make sure to get up to date on all your measles shots. You should plan to be fully vaccinated at least 2 weeks before you depart. If your trip is less than 2 weeks away and you’re not protected against measles, you should still get a dose of measles vaccine.
Source: CDC: Questions about Measles