The managers, Daniel and Amy McArthur, will not attend the hearing which is expected to last an hour at Belfast Magistrates Court.
A judge will decide procedural issues before an appeal takes place in May.
The hearing was initially set for February but was adjourned after an intervention by Northern Ireland's Attorney General.
In a previous ruling, the company was found to have discriminated against customer Gareth Lee when it said it was unable to process his order for a cake because of the message he requested to be put on it.
Mr Lee asked for a cake with the Sesame Street characters Bert and Ernie with the words 'Support Gay Marriage' above them.
The Equality Commission of Northern Ireland then brought a case against Ashers Baking Company, and in March 2015, District Judge Isobel Brownlie found Ashers directly discriminated against Mr Lee.
The couple were ordered to pay damages of £500, but subsequently appealed the discrimination verdict.
Speaking previously owner Daniel McArthur said: "We were simply unwilling to endorse a campaign for a new law that so clearly goes against what the Bible says about marriage. And for that we were punished.
"Christians are law-abiding citizens and we expect the law to protect us as much as anyone else.
"We hope that the judicial system will now make the correct decision and protect our freedom to carry out our work without being forced to violate our consciences.
"As a family we have found the whole legal process very difficult."