The court decision has to be approved by a higher court to come into effect.
The ruling will only take effect if they side with the original decision, and would only apply to the two people who brought the cases.
"This case represents another step in the fight to construct alternative drug policies that allow (Mexico) to redirect its security efforts and better address public health," MUAC said in a statement.
"We have spent years working for a more secure, just and peaceful Mexico. This case is about insisting on the need to stop criminalizing... drug users and designing better public policies that explore all the available options," said the group's director, Lisa Sanchez.
Andrés Manuel López Obrador, the Mexican president, announced soon after taking office in December last year that he planned to move towards a non-prohibitionist model on drugs, with a plan to decriminalise their use, if not production.
His National Development Plan, announced earlier this year, said "the prohibition strategy is unsustainable, not only because of violence that has been generated but because of the damage to public health."
Few expected this position to impact anything but marijuana and the recent court decision came as a surprise to observers.
Jaime Lopez, a former government security official and now independent analyst, told The Daily Telegraph that lobbyists are playing a dangerous game.
"It's a dangerous stunt that may end up emboldening and galvanizing prohibitionists," he said.
"These people have managed to draw and equivalence between marijuana and cocaine. Nobody can defend cocaine. It's harmful, non-indigenous, associated with a lot of violence. By using the same reasoning as for marijuana, they are essentially reinforcing the message that to stop marijuana is to stop all drugs."
Cocaine in the environment
Banknotes: at least 80 per cent of banknotes are thought to contain traces of cocaine, either because they have been rolled up to snort the drug, or have been contaminated by other currency.
Rivers: an estimated 4.4 lbs, roughly 80,000 lines of coke ends up in the River Thames each day via the sewage system. Italy's Po river in Milan was found to have double that amount.
Oxbridge - swabs showed cocaine at Oxford University in the Oxford Union building, the Ruskin School of Fine Art, the Oxford University Language Centre and the Bodleian library. At Cambridge University the drug was found in, 21 out of 31 toilets and washrooms.
Churches: traces of cocaine were found in 11 British cathedrals and churches, including St Paul's, St Leonard's in Shoreditch and Canterbury cathedral. St Leonard's said it tolerated drug use if it meant addicts were coming to the church for help.
Parliament: nine toilets in the Palace of Westminster have previously tested positive for cocaine including areas near MPs offices where there is no public access. In 2005 a German television station found traces of the drug in 41 out of 46 lavatories at the European Parliament in Brussels.