Thank you for the screenshot. The unstandardized coefficient is $-0.00108$ (rounded to three significant digits) with a corresponding 95% confidence interval of $(-0.00172; -0.000445)$ and a $p$-value of $0.000996$. The $p$-value is below $0.05$ and correspondingly, the 95% confidence interval does not include $0$. There is no contradiction.
The standardized coefficient is $-0.267$ but a confidence interval is not provided for this coefficient. The $p$-value does not change, however. If you're interested in calculating a confidence interval for the standardized coefficient, I have summarized the steps in my answer to another post.
As @NickCox rightly states: The predictor is probably on a large scale which leads to very small coefficients and confidence limits because the coefficients are for an increase in 1 unit. To get the change per $x$ units, divide the predictor by $x$ before calculating the regression. For example: If the predictor is money in US dollars, divide by 1000 to calculate the change for an increase in \$1000.