Does malnourishment or poor diet affect the covid-19 vaccine to not produce antibodies?

How are you defining malnourishment ? At some point the lack of proper nutrient availability will lead to many body systems breaking down including the immune response to a vaccine. Being a bit underweight, or making some poor dietary choices would not fit that definition.

Unless you are severely undernourished with multiple deficiencies, you will mount adequate response to the vaccine. For healthy diet: http://www.choosemyplate.gov/., exercise 30 minutes/day, drink enough water daily so your urine is mostly colorless, have safe sex, no tobacco alcohol weed or street drugs. Wish you good health!

I too, am perplexed by what is meant by poor diet. BUT, would absolutely not avoid vaccination because of an assumed malnourished state. The latter should be addressed, but the presence of COVID-19 would be a significantly dangerous event to be avoided.