Argyle face a winding-up petition from HM Revenue & Customs over unpaid taxes.
Todd, who was unavailable for comment, is executive chairman of software firm Ffastfill Plc and joined the Argyle board in 2009.
He was awarded a CBE in 2006 for services to the telecoms industry.
League One side Argyle face the threat of being wound up in February if they fail to pay £760,000 in unpaid tax to HM Revenue & Customs.
The club were relegated from the Championship in 2010 and have experienced dwindling attendances during their first season back in League One.
Just 4,960 fans watched their game against Dagenham & Redbridge in November - over 5,000 down on last season's average league gate.
Plymouth sit 15th in League One, just three points above the relegation places.
Source: BBC Sport
Source: BBC Sport