British Transport Police has released CCTV images of a man they want to question following the incident at The Hawthorns, in West Bromwich.
Two men were stabbed as they walked down a footpath towards the Metro station by a man who approached them at around 9pm on November 20.
Their injuries were not life-threatening or life-changing and they were discharged from hospital the following day.
The train station was cordoned off by police following the stabbing.
Detective inspector Ray Ascott, from British Transport Police, said incidents like this on the Metro are "incredibly rare".
The man in question wore a red and black North Face jacket, dark blue Under Armour jogging pants and light brown boots.
He also wore a black baseball cap, a black and white scarf and yellow rubber cleaning gloves.
The man had boarded a train at Cradley Heath station at 7.40pm earlier that same evening before arriving at The Hawthorns. He later took a train heading towards Worcester.
Anyone who sees this man is asked to call 999.
Detective inspector Ray Ascott, from British Transport Police, said: "This is a concerning act of violence which at this stage we believe to be unprovoked. We are working hard to trace the individual responsible.
"I’d appeal to anyone who may recognise the man in the CCTV image from his very distinctive clothing to get in touch with us as soon as possible.
"CCTV shows he boarded a train at Cradley Heath station at 7.40pm last Friday to The Hawthorns before later boarding a train towards Worcester.
"The man in the CCTV image is pictured wearing a black baseball cap with black and white scarf wrapped around it, a red and black North Face jacket, dark blue Under Armour jogging pants and light brown boots. He is also wearing yellow coloured rubber cleaning gloves.
"Thankfully, incidents like this on the Metro are incredibly rare and additional reassurance patrols have taken place in the area."
Anyone who recognises the man, or has any information about the attack, is asked to contact BTP by texting 61016 or calling 0800 405040 quoting reference 209-261120.
Alternatively, the Crimestoppers charity can be contacted anonymously on 0800 555111.