The 31-year-old's move from Spartak Moscow was the only incoming business concluded by the Gunners during the transfer window - yet it emerged after he joined the Gunners on loan that the midfielder is suffering from fractured vertebrae.
Arsenal manager Arsene Wenger openly concedes that Kallstrom may never play for the club, but claims to have been desperate to bring someone in on deadline day.
"I would not have signed him if we’d had two or three more days to do something. It was 5pm on Friday night, so it was sign him or nobody," said Wenger.
"There is a possibility for every single player that they will not play - but there’s also the chance he scores a winning goal that’s vitally important. We will only know if we’re wrong or right at the end of the season.”
Wenger played down the seriousness of the injury, however, and suggested that Kallstrom may be ready to play within a few weeks.
"[Being fit at the end of February] is the best-case scenario," he said. "I am sure if you have played football you might have played with a micro-fracture of your vertebra without even noticing it because on a normal scan you don't find out.
"They [Spartak Moscow] will pay the first six weeks' wages.
"He might play before that [the end of February], but he might play as well later."
Wenger blamed his desperation on the pile-up of fixtures that Arsenal face in February, which includes a 10-day spell in which they face Liverpool twice in addition to Bayern Munich and Manchester United.
"I decided to do it because we might, because of the number of games we have now in February, need the players in March or April.
"We could have gone without, but first of all you must identify a player who has the quality to play for us in January.
"Then, because we have the number of players needed in that area, [they have to be] not locked in a deal of three or four years, where you pay the players to do nothing.
"So to find a player on a free loan, of that quality, on Wednesday morning until Friday night, is not easy."
Nevertheless, Wenger accepted it was a move which could come back to haunt Arsenal as they go in search of a first trophy since 2005.
"At some stage in our job you have to make a decision. Are you wrong or right? You will only know at the end of the season," the Arsenal boss said.
"I made this decision because, since the start of the season, all our central midfielders have missed a part of the season and it can happen that a few of them miss the next part [of the season] together."
Arsenal had been linked with Schalke's £37 million-rated German midfielder Julian Draxler, but a big-money bid never materialised.
Wenger said: "We are not against spending, but at the moment we are focused on the second part of the season, and at the end of the season we will see what we will do.
"You have announced a lot of transfers in your papers that have not happened, in many places, that means it is not as easy as it looks, even with money, to buy the right players in that period."