My professor has told me he will be the corresponding author. Will it hurt my future career?

First, take time to read this question to understand what does the Corresponding Author mean for different publishers. The definitions vary, but in principle CA is the author who can be contacted about the paper results after the publication, including the long-term period (10+ years). Perhaps, you are the best person to act as a CA for this paper? Do ask yourself the following questions:

1. How certain is that you will be working in academia in the next 1 year? 3 years? 5 years? 10 years? What about your Professor?
2. If you provide your current contact details (address, email) as a CA, how likely is that your correspondence will reach you at this address in 1 year? 3 years? 5 years? 10 years? What about your Professor?
3. A CA may receive some specific questions about the study, but also broader questions about possible ways how it can be changed, adapted for a new problem, applied to a particular area in another discipline. There may be questions on how the methods used in the study compare to what other groups were doing or are planning to do. Are you fully prepared to answer these questions? What about your Professor?

If based on the answers, you decide that you are the best person to act as a CA, simply initiate a discussion with your Professor, using your answers as key points of your proposal.

It is not a problem for your career not to be the corresponding author on this paper, and there is no reason to problematise it. But you should be the first author on the author list, given what you've said about the distribution of work.