You definitely do not need a partner to learn how to dance salsa. Nearly all beginner classes accommodate students with no partners. However, having a partner is nice so that you can practice outside of class. On our group dance classes we rotate partners to practice leading and following skills. For private dance lessons, if you do not have a dance partner, you will be dancing with the instructor or assistant instructor if applicable.
In case you do have a partner, please remember that there are some advantages and disadvantages to dancing with the same person consistently. Advantages of having a partner is that you have someone to practice with on a regular basis, which is great because a lot of practice is very important. However, practicing with only one partner should be avoided, since your lead/follow will adjust to the partner's mistakes or you will learn to automatically anticipate their moves from sheer habit. So as soon as you start dancing with someone else you mayl encounter problems. While developing the leading and following skills, it is best to dance with a lot of different partners so you don’t rely on your partner to know your moves and compensate for your mistakes.