Depends on the severity, of course. Every injury is different.

Had a muscle strain in my back (near a shoulder blade) back in my late teens. Took a month to heal, without exercising, without carrying any loads. Did muscle relaxer medicine, massage. After a month, then I could begin stretching and lightly exercising again.

Up to you whether you risk it, based on what your injury's like.

Knowing what little is known, I'd suggest waiting several days with very little exercising ... at least, insofar as your back's muscles are concerned. You certainly ought to be able to, say, do a recumbent/seated bike at the gym, or other similar non-back-involved exercise for cardio. Though, I'd think any upright bike riding (gym or otherwise) would involve the back and might well exacerbate whatever's wrong.