Detective Constable James Quigley is said to have contacted Laura Johnson before she gave evidence.
The message is not thought to contain anything sexual but the fact he contacted her at all could amount to Contempt of Court.
Johnson flagged it up to her barrister during the case at Inner London Crown Court and was told she had 'done exactly the right thing' by reporting it.
The matter is now being investigated by the Directorate of Professional Standards, the Met's internal investigations unit, and will be reviewed by Judge Patricia Lees, who presided over the three week trial.
If found proved the detective could be facing possible jail time.
DC Quigley, who is an expert on gangs, gave evidence for the prosecution in the trial. He told the court what Johnson had said about possible gang links of her looting 'companions'.
DC Quigley visited her home in Orpington, Kent after the family complained that pictures taken of their house and published in the press could tip off south London gangsters where they lived.
The family had also claimed to have received anonymous letters which they believed were sent by gangs to try and intimidate Johnson before her trial.
A Met Police spokesman refused to comment on the case while investigations were ongoing.
