One of the most important challenges in text generation systems is to produce outputs that are not only correct but also diverse. Recently, Minimum Bayes-Risk (MBR) decoding has gained prominence for generating sentences of the highest quality among the decoding algorithms. However, existing algorithms proposed for generating diverse outputs are predominantly based on beam search or random sampling, thus their output quality is capped by these underlying methods. In this paper, we investigate an alternative approach -- we develop diversity-promoting decoding algorithms by enforcing diversity objectives to MBR decoding. We propose two variants of MBR, Diverse MBR (DMBR) and $k$-medoids MBR (KMBR), methods to generate a set of sentences with high quality and diversity. We evaluate DMBR and KMBR on a variety of directed text generation tasks using encoder-decoder models and a large language model with prompting. The experimental results show that the proposed method achieves a better trade-off than the diverse beam search and sampling algorithms.