Fewer than half of those using NHS Scotland's Covid-19 app who tested positive entered the code to alert other users that they should isolate.
Figures obtained by the BBC show that up to 10 December 27,239 codes were issued, but only 11,549 were uploaded.
The Protect Scotland app was launched in September and has been downloaded to more than 1.7 million phones.
The Scottish government said code uploads were consistent with other nations who used similar apps.
People who test positive for Covid-19 are given a randomly generated code to enter, which then alerts close contacts who also have the app to self-isolate.
The app also provides the contacts with advice on what to do next.
NHS Scotland Test and Protect say the app can be used to "alert people at risk far more quickly so that they can take steps to reduce the risk of infecting others".
The Scottish government said the app was monitored constantly.
A spokesperson added: "It is recognised that not all those who tested positive entered a test code into the app to enable anonymous notifications to be issued to other app users who may have been in contact.
"The upload success rate is consistent with other nations who use similar technology and contact tracing apps.
"We encourage as many people as possible to upload their test result code through the contract tracing interviews and the figure quoted includes repeat requests for test codes."
Scottish Conservative health spokesman Donald Cameron said: "This app is a key tool in Scotland's fight against Covid but yet again we learn of another serious problem.
"While the SNP government blames the behaviour of users, surely it is incumbent on them to have built an app that does the job its supposed to do."