Will a fight at work in Dubai turn into a criminal case after a complaint?

It can become a criminal case, but matters like this usually end far short of anything that threatens your visa. A shoving match is the kind of minor assault that proceeds on complaint: the police take statements from both sides, may gather CCTV from the car park, and refer the file onwards only if it is not resolved at the station. Because the incident was mutual and HR suspended you both, you are not without cards — you can file your own complaint about his part in it, and in practice mutual complaints over minor scuffles very often end in mutual waivers, with each side dropping the matter and the file closing. That is usually the smart outcome to aim for. If it does proceed, penalties for a minor altercation without injuries tend to sit at the modest end, but any conviction enters your record and can surface in good-conduct certificate applications, which is the real long-term cost worth avoiding. So attend every police appointment, give a calm and accurate account, ask early for the CCTV to be preserved before footage is overwritten, and explore reconciliation through the officers handling the file. A licensed criminal lawyer in Dubai can usually steer a two-sided case like this towards a clean closure.