The 23-year-old, who has scored three times in six appearances since returning from a knee injury, was replaced by Richie Ryan after 71 minutes of Saturday's 2-1 win at Ross County. The former Liverpool trainee, signed for United from Airdrie, is now set to be out until the turn of the year. Speaking ahead of Tuesday night's Scottish Premier League clash with Motherwell at Tannadice, Houston said:
"At the time he didn't know it was broken, his hands were so cold.
"He knew he was hurt and he came off. We took him to the hospital as soon as we got back to Dundee and unfortunately he's got two wee broken bits in his hand.
"He's going to be out for a minimum of four, maximum of six weeks. It's a blow for us and a blow for the boy because he's just come back from a knee operation.
"It's not been a great start to the season for him. These things happen sometimes in football."