In my opinion, yes. I am an undergrad Physics student (senior) and had my first contact with Fortran in my third semester, in a course called Computational Physics I. We learned the basics of Fortran 77/90 and how to solve some numerical problems using it. We also simulated some interesting problems that amazes undergrad students such as chaotic oscillators, Magnus effect in action and a few other simple yet curious systems. I had already some programming experience, but most other students didn't. They got it quite quickly and I think this is due Fortran's simplicity.
Even if you are never going to use Fortran in your own projects, you will stumble on it now and then if you are going seriously into applied and theoretical research field. NASA, for example, has tons of production code written in Fortran and even new codes are written on it. Many many Physics and Chemistry groups around the world have their most important codes in Fortran, and sometimes they use clever hacks to make the code faster, so a minimum understanding of it is necessary. I work with a Computational Chemistry group and much of the code they still develop, even for new applications, is Fortran. It is good and solid code, they are very experienced on it, and they are not willing to change to another technology so easily.
As a first language I don't know if Fortran is the best, maybe Python or Java would be my choice in this case, but it is definitely worth learning.