Qantas' engineers' union has called on the airline to ground its entire fleet of Boeing 737s after discovering a structural crack on a second of its aircraft overnight.

Qantas said on Wednesday it was undertaking immediate inspections of 33 of its Boeing 737 NGs, which have operated more than 22,600 flights, after it found a crack on one of its jets' "pickle forks", which attaches the wings to the body.

The Australian Licensed Aircraft Engineers Association said on Thursday morning that a crack in a second aircraft's primary wing structure was discovered overnight, and called for the grounding of all 75 of Qantas' 737 aircraft.

Qantas would not say whether or not it had found a crack in a second aircraft. However a second industry source, who declined to be named citing confidentiality, confirmed ALAEA's claim.