Food production and balanced nutrition will be a key challenge for residents of a future base on the Moon or Mars. As a complement to photosynthetic organisms, space aquaculture could provide the range of amino acids required to maintain health. This would rely on shipping fertilized aquaculture fish eggs to the Moon. To determine the feasibility of this, this study sought to test the influence of the conditions of a lunar mission—such as hypergravity during rocket launch and microgravity during the journey—on fish embryos and young larvae. To analyze the potential effects of these gravity changes on the early developmental stages of fish, we conducted two experiments to expose them to: i) 10 min of simulated hypergravity at 5 g (launch duration) and ii) 39 h of simulated microgravity using a random positioning machine. Both experiments used European sea bass (Dicentrarchus labrax) as a model. We analyzed egg oxygen consumption and hatching rates, as well as the expression of genes related to stress and immunity. The results indicated that neither of these altered gravity conditions affected the hatching rate. Simulated microgravity did not impact fish embryo oxygen consumption and appeared to induce faster embryonic development, as the eggs hatched earlier than expected. Levels of glucocorticoid receptors (GR1 and GR2) and heat shock proteins (Hsp90) were not impacted. Only the levels of complement component protein 3 (C3) were significantly higher in simulated microgravity, while interleukin-1β (IL-1β) transcripts were significantly lower in the hypergravity group, compared to controls. This shows that proteins involved in the innate immune system are expressed under altered gravity. Although further experiments are needed, these results suggest that the European sea bass is a promising candidate for space aquaculture.