The security breach by Norfolk County Council came to light in April 2014 when the cabinet was bought and the social work case files were found.
The Information Commissioner's Office (ICO) said the documents included information relating to seven children.
The ICO said the council had "no good reason" for breaching confidentiality.
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The council apologised for the data breach and said it had tightened procedures.
Steve Eckersley, ICO head of enforcement, said: "The council had disposed of some furniture as part of an office move but had failed to ensure that the cabinets were empty before disposal.
"Councils have a duty to look after any personal information they hold, all the more so when highly sensitive information is concerned - in particular about adults and children in vulnerable circumstances.
"For no good reason Norfolk County Council appears to have overlooked the need to ensure it had robust measures in place to protect this information.
"It should have had a written procedure in place which made it clear that any storage items removed from the office which may have contained personal were thoroughly checked before disposal."
The ICO added that having the "appropriate staff and procedures in place is key to ensuring councils look after personal information properly".
Simon George, executive director for finance and commercial services at the council, said: "We want to reassure residents that we have robust data protection procedures and have tightened practice in the light of the case published today.
"As a council we take data protection very seriously and we are very sorry that our practice fell short on this occasion.
"In the three years since this occurred, we have taken strong and effective action to ensure it is not repeated."
The county council was fined Â£80,000 in February 2012 by the ICO after a confidential social worker report was sent to the wrong address.

Ben Gilkes, 25, of Stratford Road, Sparkhill, will appear at Birmingham Magistrates Court, West Midlands Police said.
A man was arrested on Friday after the child was taken to Birmingham Children's Hospital with serious head injuries, police said.
The baby remains seriously ill since the assault in Hall Green on Friday, they added.

United ended a run of four derby defeats with a convincing 4-2 win at Old Trafford that left City with their sixth loss in their last eight games.
Pellegrini, 61, said: "It is my responsibility and the only way we can change this is by winning games.
"I am not talking about my position. It is not important."
City won the Premier League title last season and were level on points with leaders Chelsea in January, nine points above rivals United.
But they are now four points below United in fourth and face being dragged into a fight to secure Champions League football next season as Liverpool could close the gap to just four points with victory against Newcastle United at Anfield on Monday.
Pellegrini added: "The only way to explain our run is that we don't have the results. We lost many points, not only in this game which was a very difficult one, but in others too.
"We played very well for 20 minutes but we must not play just for 20 minutes, we must play for the whole game in the same way.
"We are concerned but now we must try to win the next game at home to West Ham. We have been first or second the whole year and now we are fourth but United and Arsenal have to play against Chelsea. We have 18 more points to play for. We must not be dramatic."
City faded after taking the early lead through Sergio Aguero and Pellegrini conceded that United's stirring comeback may have affected his team's fragile spirit.
"Maybe it is something we can be concerned by," he said. "It is easy when you are two goals in front to play with more trust than the team that is two goals behind.
"We made important mistakes for the second goal and the third was offside but the result was a fair one."

Tens of thousands of Wales supporters travelled to France in the summer to see their side progress to the tournament's semi finals.
They were branded "the red wall" by the Wales players.
Uefa's executive committee has also recognised supporters from Iceland, Republic of Ireland and Northern Ireland.
The announcement coincides with Wales rising to 10th in the Fifa world rankings.
A council has been fined Â£60,000 for leaving confidential files about vulnerable children in a cabinet which was sent to a second-hand shop.
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A man is due in court charged with an assault on a four-week-old baby boy.
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Manchester City manager Manuel Pellegrini took full responsibility for his side's alarming slump but refused to discuss his long-term future.
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Wales football fans have been given an "outstanding contribution" award from Uefa for their part at Euro 2016.