After messing around for a while to figure out a way to do this, eventually I figured it out using the EXISTS clause.

Here is an example :

UPDATE tbl1
SET tbl1_field = ( SELECT tbl1_field
FROM tbl1
WHERE tbl.tbl1_id = tbl2.tbl2_id)
WHERE EXISTS
( SELECT tbl1_field
FROM tbl1
WHERE tbl.tbl1_id = tbl2.tbl2_id);