The oilfield services group's shares were down 5.62 per cent at 588p in morning trading.
In June, Wood Group's shareholders approved a £2.2bn merger with Amec Foster Wheeler. The takeover is expected to complete in the fourth quarter this year.
The SFO opened an investigation into Amec Foster Wheeler, predecessor companies and associated persons in respect of the Foster Wheeler business yesterday.
"As announced by Amec Foster Wheeler, the investigation focuses on the past use of third parties and possible bribery and corruption and related offences," Wood Group said in a statement.
"In its circular and prospectus published on 23 May 2017, the company disclosed that information previously provided by Amec Foster Wheeler to the SFO related to matters that may well develop into an investigation into Amec Foster Wheeler by the SFO."
Wood Group acknowledged that it is not possible to estimate reliably what effect the outcome of the matter will have on Amec Foster Wheeler.