After changing the hub and bearing assembly on a 2013 Mazda 3, the ABS warning light on the dash stayed lit. What might be wrong?

Did you hookup the ABS pigtail?

A few things to look at. The front bearing is a replacement bearing only, not a hub assembly. One possibility is the wrong bearing. The ABS compatible bearing has a magnetic ring in it that works with the sensor. If a non abs bearing was installed The sensor wont read wheel speed. Second is an improperly installed bearing. IF it was put in with the magnetic ring facing away from the sensor it will not read. If it was pressed in improperly It could have broken the magnet. If it was hammered in. The magnet is definitely broken. If the bearing is not seated all the way into the spindle The sensor wont read the magnet. Lastly If the sensor was not removed from the spindle It is now broken and needs to be replaced. If the sensor was stuck in the spindle and had to be pried out. There is a better than good chance that it is broken internally. Lots to check out. But I hope this helps.

The bearing and hub were purchased as a unit - bearing already installed in the hub. The only thing I had to change over from the old hub was the little unit in the back of the hub that the wire plugs into. This little unit is black and rectangular in shape - I assume this is the sensor?

That is the sensor. They are easily broken. Also if the hub was purchased used. It might be bad, or the non abs version.

A broken wire is a possibility. It is a rear hub and bearing purchased new and the light came on immediately after installation.

There was no sensor with the new part. I removed it from the old hub and installed it in the new one. I can purchase a new sensor and try it.

That's probably the easiest way to solve this problem. The sensors are delicate and if it was stuck in the hub in any way there is a very good chance it's broken internally.

2011 mazda 3 I did change front wheel bearing after that abs light is on