The post was removed because of a copyright complaint.
It featured a doctored version of the band’s 2015 music video Photograph, showing singer Chad Kroeger holding a photo of Mr Biden, his son, a Ukrainian gas executive and another man.
Mr Trump’s tweet came as the president has repeatedly criticised Democrats for launching an impeachment inquiry into his telephone call with Ukraine’s president in which Mr Trump pressed for an investigation of his Democratic rival Mr Biden and his son.
A Twitter spokeswoman said on Thursday it responded “to valid copyright complaints sent to us by a copyright owner or their authorised representatives”.
Nickelback representatives have not returned messages seeking comment.