A spokesman for the Israel Defence Forces said that the air force had targeted two sites in the central and southern Gaza Strip. Direct hits were confirmed.
Earlier, 20 foreign delegates and hundreds of Israeli dignitaries had attended a state memorial service for Mr Sharon in Jerusalem.
They included US Vice President Joe Biden and Middle East international envoy Tony Blair.
Israel's Prime Minister Benjamin Netanyahu said Mr Sharon was "one of the greatest military commanders the Jewish people have had".
Mr Biden described him as an "indomitable bulldozer... The security of his people was his unwavering mission".