That's a valid question. Respiration definitely requires oxygen in plant tissues. Plants can take up oxygen during the day, however, when they are photosynthesizing, they generally don't have to. This is because the photosynthetic reactions split water (H₂O) into hydrogen and oxygen, forming O₂ gas. This oxygen is then used in respiration inside the plant tissues.

During the day (with plenty of sunlight there actually becomes too high of an oxygen concentration inside the plant and a lot of O₂ diffuses out of the plant tissues. At night, there is no photosynthesis and so there is a net uptake of O₂ and release of CO₂ (from respiration). It's as if the plants are taking one deep breath in during the day and exhaling at night, but they grew during the day and incorporated some CO₂, so the breath in is bigger than the breath out.

Check out this image for a basic summary:
plants respiration

Plants generally take in oxygen at night when they can't photosynthesize. During the daytime, they can get light and use that for energy. Very young plants can also have energy reserves in their seeds still.