The Construction, Forestry, Mining and Energy Union has been fined more than $46,000 for ordering stop work action at a Melbourne construction site.

The Federal Magistrates Court heard union organiser Adrian McLoughlin directed workers to stop work at a $45 million apartment project in 2008.

The court penalised the CFMEU $38,500 and Mr McLoughlin nearly $8,000 for the unlawful industrial action.