CodeIgniter is licensed under an Apache/BSD-style open source license so you can use it however you please. For more information please read the license agreement.

[...] So it seems that, while CodeIgniter doesn’t use a standard open source license and could be doing more to protect the open source status of derivative works, it does qualify as open source. Using a more recognized open source license might help others have confidence in this fact; so would being certified by the Open Source Initiative.