It comes after a new report highlighted a string of issues on the line between Edinburgh and Tweedbank.
MSP Christine Grahame asked what steps the Scottish government would take in light of its findings.
Mr Yousaf said ScotRail's improvement plan had a focus on the Borders Railway and he would be reviewing its progress.
He said he wanted to ensure that better performance was delivered.
The SNP's Ms Grahame also raised the issue of the number of cancellations on the route and asked whether the recovery plan was actually having any effect.
"When an improvement plan is put in place, we have to give ScotRail the time to be able to enact it, and a serious amount of work is going into that," said Mr Yousaf.
"For example, Â£14m is going into the refurbishment and improvement of the class 158 units."
However, he said he was not going to be satisfied until the Borders Railway reached its public performance measure targets and some of the problems were resolved.
"An improvement plan is in place, significant funding is going into that and we are going to give ScotRail the time to ensure that its performance improves," he said.
"I will monitor that closely and if it does not improve, there will be consequences."
He also added that he was happy to discuss concerns with campaigners.
South of Scotland Conservative MSP Rachael Hamilton raised the issue of six requests made by campaigners to improve services.
They include increasing the number of coaches on busier services and replacing defective radiators.
Mr Yousaf said that the requests were "very reasonable" and that ScotRail was taking them forward.
He said there should be more capacity on the network at peak times in 2017.
"All those asks are very reasonable and ScotRail is acting on them," he said.
Mr Yousaf also stressed it was important not to lose sight of the "great success" the railway had proved to be.
"There have been over one million passengers and it is the longest new rail line in a century," he said.
"There has been great success, which has been celebrated.
"Notwithstanding that, there are some issues that ScotRail is determined to get to the bottom of, and I will personally keep an eye on that."
Transport Minister Humza Yousaf has said he will be "closely monitoring" efforts to improve performance on the Borders Railway.