The meta-analysis also looked at the impact of medicinal cannabinoids on Tourette's syndrome, post-traumatic stress disorder and psychosis.
Research which combined 83 studies involving 3,000 people suggested their use for the six mental health conditions cannot be justified based on the current evidence.
Scientists said this is due to a lack of evidence for their effectiveness and because of the known risks of cannabinoids.
But the study, published in the Lancet Psychiatry journal, suggests there is very low quality evidence that pharmaceutical tetrahydrocannabinol (THC) may lead to a small improvement in symptoms of anxiety in individuals with other medical conditions.
Professor Louisa Degenhardt of the National Drug and Alcohol Research Centre (NDARC) at UNSW Sydney, Australia and the study's lead author said: "Our findings have important implications in countries where cannabis and cannabinoids are being made available for medical use.
"There is a notable absence of high-quality evidence to properly assess the effectiveness and safety of medicinal cannabinoids compared with placebo, and until evidence from randomised controlled trials is available, clinical guidelines cannot be drawn up around their use in mental health disorders."
Medicinal cannabinoids include medicinal cannabis and pharmaceutical cannabinoids, and their synthetic derivatives, THC and cannabidiol (CBD).
They are increasingly being made available for medicinal purposes in countries like the United States, Australia and Canada, including for the treatment of mental health disorders.
However, researchers say there are concerns around the adverse effects of this availability.
They say this is due to a large body of evidence indicating that non-medicinal cannabis use can increase the occurrence of depression, anxiety, and psychotic symptoms.
The authors analysed published and unpublished studies between 1980 and 2018.
Of the 83 eligible studies, 40 were randomised controlled trials (RCTs), and the others were open-label trials, where participants knew which treatment they were taking.
In most RCTs examining depression and anxiety, the primary reason for cannabinoid use was for another medical condition such as chronic non-cancer pain or multiple sclerosis.
The cannabinoid was used to treat the mental health disorder in the studies that looked at the other four disorders.
Only a few RCTs looked at the role of pharmaceutical CBD or medicinal cannabis - most looked at THC, with or without CBD.
Researchers found pharmaceutical THC (with or without CBD) improved anxiety symptoms among individuals with other medical conditions. However, this may have been due to improvements in the primary medical condition.
The authors suggest further research should study the effects of cannabinoids on anxiety and depression.
According to the analysis, pharmaceutical THC - with or without CBD - worsened negative symptoms of psychosis in one study of 24 people, and did not significantly affect any other primary outcomes for the mental health disorders examined.
It also increased the number of people who had adverse events and withdrawals due to adverse events, compared with placebo across all mental health disorders examined.
Scientists say there is a need for high-quality research to understand the effects of different cannabinoids on a range of outcomes for people with mental health disorders.
They highlight that their analysis and conclusions are limited by the small amount of available data, small study sizes, and the differences in findings between small studies.
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