Correlations between the intrinsic shapes of galaxy pairs, and between the intrinsic shapes of galaxies and the large-scale density field, may be induced by tidal fields. These correlations, which have been detected at low redshifts (z < 0.35) for bright red galaxies in the Sloan Digital Sky Survey (SDSS), and for which upper limits exist for blue galaxies at z∼ 0.1, provide a window into galaxy formation and evolution, and are also an important contaminant for current and future weak lensing surveys. Measurements of these alignments at intermediate redshifts (z∼ 0.6) that are more relevant for cosmic shear observations are very important for understanding the origin and redshift evolution of these alignments, and for minimizing their impact on weak lensing measurements. We present the first such intermediate-redshift measurement for blue galaxies, using galaxy shape measurements from SDSS and spectroscopic redshifts from the WiggleZ Dark Energy Survey. Our null detection allows us to place upper limits on the contamination of weak lensing measurements by blue galaxy intrinsic alignments that, for the first time, do not require significant model-dependent extrapolation from the z∼ 0.1 SDSS observations. Also, combining the SDSS and WiggleZ constraints gives us a long redshift baseline with which to constrain intrinsic alignment models and contamination of the cosmic shear power spectrum. Assuming that the alignments can be explained by linear alignment with the smoothed local density field, we find that a measurement of σ8 in a blue-galaxy dominated, CFHTLS-like survey would be contaminated by at most +0.02−0.03 (95 per cent confidence level, SDSS and WiggleZ) or ± 0.03 (WiggleZ alone) due to intrinsic alignments. We also allow additional power-law redshift evolution of the intrinsic alignments, due to (for example) effects like interactions and mergers that are not included in the linear alignment model, and find that our constraints on cosmic shear contamination are not significantly weakened if the power-law index is less than ∼2. The WiggleZ sample (unlike SDSS) has a long enough redshift baseline that the data can rule out the possibility of very strong additional evolution.