I'm currently completing my Master's coursework and thesis (at a university in the United States). My employer plans to submit an H-1B petition for me on April 1 for the next year's quota/cap. My university's graduation ceremony is in May, at which time I'll have my degree. Will the timing of all this present any problems?
Your employer may be able to submit the H-1B petition for you as planned. There are several things to consider.
The basic requirement at issue here is that the employer must submit a complete H-1B petition on your behalf. Submitting a petition before you and your employer meet the requirements for an H-1B visa (e.g. by not having a degree as of the time of submitting the petition) normally leads to a denial of the petition. See "Common Reasons for Denial of an H-1B Visa" for more on H-1B petition denials.
First, talk to your academic advisor to determine whether you will have completed the degree requirements by April 1. If yes, ask your college or university whether the registrar or department chair will issue a letter confirming that you have completed the requirements for the degree. That letter and your transcript will be enough to satisfy U.S. Citizenship and Immigration Services (USCIS) that you have earned the degree.
Second, if you have not completed the degree requirements as of the date your employer submits your H-1B petition, or if you cannot obtain a letter from your university to confirm your completion of the degree requirements, you may be able to rely on another degree for the H-1B petition.
For example, if you're working as an engineer and already have a relevant Bachelor's degree in engineering (either from the U.S. or a foreign equivalent degree – see "H-1B Visa to the U.S.: Who Qualifies?" for more on the degree requirement), that may be enough of a basis upon which to submit the H-1B petition. As long as the job requires only a Bachelor's degree, your Master's degree is not necessary for the H-1B petition.
Finally, as you may be aware, having a Master's degree would allow you to qualify for the first 20,000 visas that are exempt from the H-1B cap. Therefore, if possible, it is to your advantage to document your completion of the Master's degree. If USCIS receives more petitions than there are visas available, your Master's degree gives you two chances at getting a visa. USCIS first allocates the 20,000 U.S. graduate degree petitions. USCIS then adds any graduate degree petitions over that amount to the remaining pool to allocate the remaining 65,000 visas.