One references Basquiat’s 1982 Boy and Dog in a Johnnypump, showing a boy being searched by police officers.
“Portrait of Basquiat being welcomed by the Metropolitan Police - an (unofficial) collaboration with the new Basquiat show,” Banksy said of the work on his official Instagram feed.
The second depicts people queueing up to ride a Ferris wheel with carriages shaped like crowns, referencing Basquiat’s 1983 Crown.
The Barbican show Basquiat: Boom for Real, is the first large-scale exhibition in Britain of the work of the artist, who rose meteorically in 1980s New York and died, aged 27, of a drug overdose.
A 1982 Basquiat painting of a skull sold for $110.5million (R1.4 billion) in May.
“Major new Basquiat show opens at the Barbican - a place that is normally very keen to clean any graffiti from its walls,” Banksy said.
Banksy, whose keeps his identity secret, rose to prominence through street art, in the English city of Bristol, in the 1990s.
His works, often stencilled onto the outside walls of buildings, combine humour and social commentary.