15 week old Esme Emmerson was travelling home from a day out in Beverley with her father and mother Jason Emmerson and Kristina Vojsovicova on the 3pm Northern service from Bridlington to Hull when the incident happened close to Snuff Mill Lane at 3:45pm.
Northern and British Transport Police have now issued an appeal for information.
Tony Baxter, regional director for Northern, said: “This was a totally reckless act by mindless individuals who gave no thought for other people’s safety.
“The consequences of a brick hitting a fast-moving train are potentially devastating and we can only give thanks that Esme wasn’t more seriously injured.
“Someone must know who threw that brick and I urge anyone with information about the events that led to Esme being hurt to contact British Transport Police.”
Esme’s parents said: “It all happened so quickly. We were almost arriving into Hull when the brick hit the window and the smashed glass fell into Esme’s pram. We were in shock. I’m just so grateful that Esme wasn’t seriously hurt. I want whoever did this to know the impact of their actions. They need to hand themselves in to the police.
“It’s a reminder to all parents to make sure to keep your kids safe as anything can happen while travelling with people doing this crazy stuff.
“That brick could have hit Esme or one of us – but thank god our baby is safe.”
Chief inspector Graham Bridges said: “This was a very serious incident that could have had devastating consequences. Passengers, including a tiny baby, could have been seriously injured by the actions of whoever threw this object.
“Throwing bricks and stones at trains is an incredibly dangerous and reckless thing to do. We are working hard to identify those responsible.”
Anyone with information can contact BTP by texting 61016 or by calling 0800 40 50 40. Alternatively, people can call Crimestoppers, anonymously, on 0800 555 111.