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Variations of this idiom with the same meaning:

can’t carry a tune in a bucket;

can’t carry a tune in a bushel basket;

can’t carry a tune in a paper sack.

Examples from the web:

• Mark: “Sing with us!”
  John: “Sorry. You wouldn’t want me to. I can’t carry a tune.”
• I invited Sarah to join the choir but she refused, she told me she can’t carry a tune in a bucket.

A short article I found while surfing the web: “Can’t Carry a Tune? Work Out Your Vocal Muscles”. by Lena Groeger
This is the link (I opened it with Lingro, in this way if you click on a term that you don’t know, you can read the definition in English): http://lingro.com/translate/http://www.scientificamerican.com/article/physically-out-of-tune/
In short, the article is about physical reasons of bad singing.