The move comes after the Forth Road Bridge was closed for 19 hours when a lorry was blown over last month. The driver was charged with dangerous driving because the lorry overturned.
However, other motorists who ignore vehicle bans during bad weather cannot be prosecuted unless they commit another offence, such as crashing.
Transport minister Humza Yousaf said: “I have asked Transport Scotland to examine how often this is happening and what enforcement measures we can take.
“There needs to be some honest conversations with heavy goods vehicle operators.”
A spokeswoman for the Scottish Government agency added: “Drivers of high-sided vehicles must act responsibly in windy conditions and comply with the warning signs or they risk being prosecuted for dangerous driving.
“We are reviewing the recent incident at the Forth Road Bridge and the wider implications for other crossings with our operational partners, with our focus on working alongside the industry to address the issues.
“In particular, we are looking to establish a clearer picture of the extent of non-compliance and this will inform our next steps in terms of education and deterrent measures.”
Police Scotland confirmed that wind restrictions, such as on bridges, were advisory.
These are similar to electronic variable speed limit signs on overhead motorway gantries in Scotland, except for those displayed within red circles, such as on approaches to the Forth Road Bridge – which are compulsory.
Superintendent Fraser Candlish, the deputy head of road policing, said: “There is no specific offence for failing to comply with a high wind warning.
“However, it is likely that the driver of any high-sided vehicle who ignores warnings and is thereafter involved in a wind-related incident could be charged with careless or dangerous driving, depending on the circumstances.”
The national force launched a safety campaign to prevent lorries being blown over on other roads in October after Scotland on Sunday revealed ministers had ordered an investigation following 11 incidents within weeks last winter.
Hauliers have been urged to drive with curtain-sided wagons tied open if they are empty to cut the risk.
Forth Road Bridge officials said they had fine-tuned their high wind procedures over the five decades since the crossing opened, and these had proved to be highly effective.
They pointed to the fact that only a handful of vehicles have ever overturned out of more than 200 million which have crossed the bridge.
However, the impact of a crash can be major, since the bridge is used by nearly 70,000 vehicles a day.
The IAM RoadSmart motoring group – the former Institute of Advanced Motorists – said it supported a crackdown so long as more signs were installed and drivers could challenge being charged.
Neil Greig, its Scotland-based policy and research director, said: “We would support tougher penalties for lorry drivers who deliberately drive past ‘road closed to high-sided vehicles’ signs.
“There must be a right of appeal, however, and a strong commitment from Transport Scotland to provide more electronic signposting and accurate weather forecasting.”