The Advertising Standards Authority (ASA) said it started the inquiry into the Home Office's "go home or face arrest" vans following 60 complaints.
The pilot scheme has faced criticism from the Liberal Democrats and Liberty.
A Home Office spokesman said it was in contact with the ASA and would "respond in due course".
Communities Secretary Eric Pickles told BBC Radio 5 live that the scheme would be rolled out nationally, "if proved effective".
He said: "Given Labour's open-door immigration policy, I don't see anything offensive as suggesting to illegal immigrants that their stay in this country might be shorter than they thought."
The Home Office has said the pilot worked, but did not say how many people had left the country.
Vans were driven around Barnet, Hounslow, Barking and Dagenham, Ealing, Brent and Redbridge as part of the campaign, which started on 22 July and lasted a week.
In a statement, the ASA said complainants had expressed concerns that the advert, in particular the phrase "go home", was offensive and irresponsible.
It said complainants were concerned this was "reminiscent of slogans used by racist groups to attack immigrants in the past and could incite or exacerbate racial hatred and tensions in multicultural communities".
