problem is position of tikzpicture baseline (which is in the middle of the circle). you should move it accordingly. the simplest way seems to be enclose image in adjustbox. a bit shorter code you obtain if instead two minipages use tabular environment. however use of adjustbox work in combination with minipage:
\documentclass{article}
\usepackage{tikz}
\usepackage{adjustbox}
\begin{document}
\centering
\begin{tabular}{|p{0.25\linewidth}|p{0.5\linewidth}|}
$2+2=4$
&
\adjustbox{valign=t}{\begin{tikzpicture}% adjustbox move tikzpicture baseline to the top of tabular cell
\draw (0,0) circle (3cm);
\end{tikzpicture}}
\end{tabular}
\end{document}
or
\documentclass{article}
\usepackage{tikz}
\usepackage{adjustbox}
\begin{document}
\centering
\begin{minipage}[t]{0.25\linewidth}
$2+2=4$
\end{minipage}
\adjustbox{valign=t}{\begin{tikzpicture}% adjustbox move tikzpicture baseline to the line in in minipage
\draw (0,0) circle (3cm);
\end{tikzpicture}}
\end{document}
