All surfaces have their positives and negatives. As for grass, the obvious positive is that it is much more cushioning than most surfaces, especially paved surfaces. The negatives are that it is a less even surface and that it requires more strength, especially lower leg strength, to run through.
Off the top of my head, I can't recall what your injury was. If it was an impact related injury, hitting some grass trails might be beneficial. The only thing I'd suggest is building into it gradually. Once a week might be a good start. Another way to work it in would be to add some time on grass to some of your daily runs.
Another option if you're used to paved surfaces would be to consider dirt trails if some are available to you. These would be softer than paved surfaces but be more consistent and even, so you could transition to them more quickly than grass with less risk of developing a lower leg or ankle problem. Around here, we have some crushed, compacted limestone trails. These are softer than pavement but are very consistent and even so you don't have to worry about twisting an ankle or, if you're used to paved surfaces, overworking the stabilizing muscles in your lower legs. The transition from pavement to this type of surface shouldn't take long at all.