The man was transferred from Altnagelvin Hospital to the Royal Victoria Hospital in Belfast to be treated for serious burns injuries.
He is said to be in a stable condition.
Deputy mayor of the city Gary Middleton, who is at the scene, wrote on Twitter: "Fire service working hard to extinguish flames. Residents who have been evacuated from Bond Street are currently staying with family and friends."
A police spokesman said the area was expected to remain cordoned off overnight.
COMMENT RULES: Comments that are judged to be defamatory, abusive or in bad taste are not acceptable and contributors who consistently fall below certain criteria will be permanently blacklisted. The moderator will not enter into debate with individual contributors and the moderator’s decision is final. It is Belfast Telegraph policy to close comments on court cases, tribunals and active legal investigations. We may also close comments on articles which are being targeted for abuse. Problems with commenting? firstname.lastname@example.org